Metonymy processing ability is an important pragmatic skill. The cognitive abbreviation of metonymy greatly facilitates communication, and is a common way of communication for typically developing (TD) individuals in daily life. Studies have found that children's metonymy processing ability will keep improving with age. Children with high functioning autism (HFA) are obviously inadequate in comprehension of metaphorical language. Will they improve their metonymy processing ability with age like TD children, whether the development of conventional metonymy and novel metonymy is the same, and whether the neural mechanism of their processing metonymy is different from that of children with TD has not been explored. This study used event-related potential technology to explore the cognitive processing mechanism and developmental trajectory of conventional and novel metonymy in children with HFA aged 6~11 years. The experiment selected 30 HFA children aged 6~11 years old, of which 15 were 6~8 years old and 15 were 9~11 years old. The same was done for the control group. The four groups of children's age and Webster's intelligence scores for children all have a statistically good match. The materials were divided into 4 categories: conventional metonymy, novel metonymy, literal sentences, and error sentences, each with 32 sentences. The materials were presented on a computer in 3 screens of subject-verb-object, and EEG signals during the experiment were collected. The ERP results showed that: both 6~8 years old and 9~11 years old HFA children’s N400 amplitudes of conventional metonymy and novel metonymy were lower than that of TD children of the same age, this suggests that HFA children have more difficulty in processing metonymy than TD children of the same age. There was no significant difference in the N400 amplitudes of conventional metonymy and novel metonymy between HFA children aged 6~8, the N400 amplitudes of conventional metonymy and novel metonymy were not significantly different from the error sentences. 9~11 years old HFA children's N400 amplitudes of novel metonymy were less than conventional metonymy, there is a conventional degree effect, which suggests that HFA children of this age have been able to recognize the difference between conventional and novel metonymy. The N400 difference amplitudes of HFA children aged 6~8 years for conventional metonymy were less than that of HFA children aged 9~11 years, there was no significant difference for novel metonymy. This shows that from 6 to 11 years old, 9~11 years old HFA children are easier to process conventional metonymy than 6~8 years old. For novel metonymy, 9~11 years old is as difficult as 6~8 years old. The present study suggests that HFA children's processing of conventional and novel metonymy lagged behind that of TD children overall. Although both conventional and novel metonymy processing was poor in HFA children aged 6~8 years, conventional metonymy processing improved in HFA children aged 9~11 years, while novel metonymy processing remained poor. From 6~11 years old, HFA children's conventional metonymy processing improved significantly with age, while novel metonymy did not show significant improvement, and the processing of novel metonymy was particularly difficult compared to conventional metonymy.