Last year ,after he graduated from university,he went to study chinese at PeKing university.

Last year 是过去时间提示词,所以整个句子都跟过去时间有关.又因为主句和从句有先后关系,所以也可以用主句是过去时,而从句是过去完成时.Last year,after he had graduated from university,he went to study Chinese at Peking University.
但是,如果强调他大学一毕业就入北京大学学习汉语,那么就用用主句是过去时,而从句也是过去完成时.Last year,after he graduated from university,he went to study Chinese at Peking University.
后者更加符合我国教育的实际情况.同时也可以写成Last year,after graduating from university,he went to study Chinese at Peking University.