Negative memory bias is one of the prominent cognitive deficits in depression. Previous studies mainly focused on the bottom-up selective attention to negative information in depressive individuals or the patients with depressive disorder. The influence of the top-down executive control deficit on memory has been largely ignored. Recent studies indicate that the deficit of memory suppression plays an important role in the formation and maintain of negative memory bias in depression. The main reason that depressive individuals persistently and negatively ruminate is that they cannot effectively perform motivated forgetting of negative events/stimuli. The relevant study will be of great importance in the improvement of the cognitive model of depressive disorder and the planning of therapeutic schedules for patients. The current mini-review introduced recent studies on memory suppression (or motivated forgetting) in healthy adults and in individuals with depressive disorder/tendency. In general, there are two stage of memory suppression, namely the encoding stage and the retrieval stage. As regard to the memory suppression on the encoding stage, directed forgetting paradigm is usually employed to compare the number of remembered items between to-be-remember and to-be-forget conditions. The effect of directed forgetting in healthy subjects is reflected by the performance in the posttest, which shows that the remembered items are more in the to-be-remember condition, compared with the remembered items in the to-be-forget condition. Recent studies in healthy adults revealed that the effect of directed forgetting is not only due to the mechanism of selective rehearsal, but also associated with the motivated forgetting in the memory encoding. As regard to the memory suppression on the retrieval stage, think/no think paradigm is usually employed to compare the number of remembered cue-target pairs between think and no think conditions. The suppression-induced forgetting can be observed when healthy subjects perform the think/no think task. In particular, the cue-target pairs in the no think condition are less frequently recalled in the posttest, as compared with the cue-target pairs in both the think condition and the baseline condition. Behavioral studies of memory suppression in depressive subjects have revealed that inhibitory control deficits exist on both memory encoding and retrieval stages. More specifically, three studies used directed forgetting paradigm found that compared with healthy controls, 1) individuals diagnosed with depression remembered fewer to-be-remember items while they forgot fewer to-be-forget items; 2) the patients remembered more negative than positive words in the to-be-forget condition; and 3) the impaired memory suppression for negative words was positively correlated with the severity of negative rumination. At the same time, three studies used think/no think paradigm found that the more severe the negative rumination, the worse performance of subjects in the no think condition. Furthermore, compared with healthy controls, depressive subjects remembered more emotional, especially negative, words in the no think condition. According to the current finding reviewed in this paper, we proposed three problems that need to be solved in this area and discussed possible solutions. It is suggested that directed forgetting and think/no think paradigms are employed simultaneously to explore the neural mechanism of the deficit of memory suppression in depression. Electroencephalogram and functional magnetic resonance imaging are appropriate techniques, which facilitate us to compare the spatial-temporal pattern of event-related potentials, event-related oscillations, and blood oxygen level dependent signals during the emotional memory suppression task in depressive individuals and healthy controls. In addition, repetitive transcranial magnetic stimulation is suggested to use in the experiment; it can stimulate specific brain region(s) so as to help illuminating the causality of specific brain region(s) in the deficit of memory suppression in depressive individuals.