The purpose of this study is to investigate the differences among mother\'s feeling expression, children\'s self-regulation, and children\'s peer competency by socio-demographic background and provide a basic material to develop the parents\' education for mother\'s promosing emotional environment to help development of children by understanding the correlation among mother\'s feeling expression children\'s self-regulation, and children\'s peer competency. The research objects were 361 of 4 to 6-year-old children and their mothers. The tool adapted by Woo Sookyong(2002) was used for Mother\'s emotional expressivity, and the tool of Lee Jeongran(2003) for the of self regulation and the tool of park Joohee and Lee Eunhae for the children\'s peer competency. Data analysis was performed with population, percentage, t-test, Cronbach ⍺, F-test, and co-relation of LSD posteriori test. The summary of this study are as follows; First, the more negative expressivity was shown as mother\'s academic career was higher and the more positive one was appeared as family income was greater according to the background of socio-demography. Female children showed the higher self-regulation, and the self-decision and action control were greater as their age was higher. Children\'s peer competency was higher as they were social and friendly personality. Second, there was the strong relationship among the mother\'s feeling expressivity, children\'s self-regulation and peer competency one. Mother\'s positive expressivity had the relationship with children\'s self-regulation and peer competency one while weak expressivity had it with self-decision, regulation and children\'s peer competency. But the strong negative heartstrings\' expressivity was an improper co-relation with action control and no relation with similar age competent ability. A definitive relation existed between all low level area except the emotion of self-regulation and children\'s peer competency. Form the above study, it was Known that there was the relationship among the mother\'s feeling expressivity, children\'s self-regulation and peer competency. In particular, there was strong relationship between positive and weak positive expressivity, and children\'s self-regulation and peer competency. These results could be reflected to parents\' heartstrings education by knowing the impact of a positive emotional expressivity and weak-negative one.