The father child relationship as one of the three major relationships in the family had varying degree of influence over all aspects of children’s development, especially the development of the social behavior. The purpose of this study is to explore the development of 4~6 year old children's social behavior (including sharing behavior and the behavior problems) and its relation with the father-child relationship. On one hand the present study can promote people’s understanding of the issue. On the other hand it can provide scientific foundation for education to help build a better father-child relationship, make the family more harmonious and children develop more healthily. This study recruited 102 cases of 4~6 year old children in one Beijing nursery school, using a modified version of the dictator game of sharing behavior and Child Behavior Checklist (CBCL) measurement problem behavior. Study the relationship between father and son is the use of the family relationship indication scale (Family Relations Indicator, FRI). The main results are as follows: 1、There was no age and sex difference in sharing behavior of children aged 4~6 in the stranger situation or friends scenario. They were also more willing to distribute fairly with friends. Father-child relationship will affect children’s distribution with friends. But the items distributed to strangers were not different significantly among children in different kind of father-child relationship. Children with positive father-child relationship distributed more to friends than those with neutral or negative father-child relationship. Boys in negative relationship with father gave less to their friends, compared with girls in the same father-child relationship. 2、Children in negative relationship with father showed more problem behavior and withdrawn behavior. Boys’ problem behavior was more related with their father-child relationship, compared with girls. The children with negative relationship between father and son showed more problem behavior and withdrawal behavior. Compared with girls, boys have more problem behaviors and parent-child relationship more closely linked. In conclusion, this study confirms that parent-child relationships can predict children's sharing behavior positively, and negatively predict children’s problem behavior. Negative father-child relationship has a bigger influence over boys than girls.