Intentional forgetting refers that individuals intentionally forgot useless or outdated information, which is important for human life and memory updating. In recent years, intentional forgetting research has become a hot topic, both domestic and abroad research findings about intentional forgetting become richer, but system introduction and conclusion about brain mechanism of intentional forgetting is lacked. Therefore, based on related findings, we respectively introduced the brain mechanism of directed forgetting and suppression forgetting. The brain mechanism of directed forgetting was mainly reflected in encoding and retrieval phase. In encoding phase, different instructions caused different brain activities, R (remembering) instruction caused activation of memory processing region, while F (forgetting) instruction caused activation of inhibitory region. These different brain activities supported attention inhibition theory of directed forgetting, which believed that directed forgetting was because participant actively inhibited rehearsing and processing of F item. In retrieval phase, different old/new effects existed between TBR-R (to be remembered-remembered) items and TBF-R (to be forgotten-remembered) items, the former were based on recollection, and the latter were based on familiarity. While TBF-F (to be forgotten-forgotten) items induced reversed old/new effects, which indicated that need to forget items was inhibited in retrieval phase, so retrieval inhibition is also an explanation of directed forgetting. In a word, the brain mechanism research of directed forgetting showed that directed forgetting is an active inhibition process, encoding inhibition and retrieval inhibition both play important role in directed forgetting. The brain mechanism of suppression forgetting mainly reflected in differences between think items and No think items. Think items and No think items respectively activated different brain areas, think items increased activation of hippocampus and other memory-related brain areas, while No think items increased activation of prefrontal cortex and reduced activation of hippocampus. The existing suppression forgetting explanation is prefrontal-hippocampus assumption, which considered that individuals will firstly induce activation of prefrontal cortex and subsequently inhibit activation of hippocampus so as to achieve the goal of inhibiting unwanted memory. Though the present review illustrated the brain mechanism of directed forgetting and suppression forgetting, there were still many problems to be solved. Future research should focus on：the brain mechanism differences of directed forgetting and suppression forgetting; the brain mechanism differences between memory inhibition and other psychological suppression; intentional forgetting of traumatic experience and mental illness individuals; plasticity research of memory control network.