This study was conducted to analyze the effects of family background factors and individual characteristic variable on longitudinal changes in mathematics achievement by high school type in Seoul using data from the 1st year and 7th to 9th years of the SELS elementary school panel. Two-level multi-level growth model was used. First of all, General High school(GHS) students’ math achievement increased during the 3 years of high school, there was no significant change in math achievemnt of Special Purpose Highg School(SPHS) and Autonomous Private High School(APHS). In addition, the effect of the family background on the initial mathematics achievement of GHS students was significant, but the effect of the family background was not significant for SPHS and APHS students. It was found that the effect of the family background on the rate of change in mathematic achievement was found to have a negative effect on every type of high school. However, as a result of analyzing the interaction effect by group according to the family background, it was found that the effect of parental education level was reversed only for SPHS and APHS students during three years of high school. There has been a perception that the transfering SPHS and APHS to GHS will strengthen the equity of education, but in fact, it is only a difference between whether the effect of family background will have affect on the 'entry stage' of high school or 'while attending high school'. It turns out that this may have nothing to do with strengthening equity in education. However, problems such as ‘Cream-skimming’ and ‘stratification between schools’ due to SPHS and APHS still exist, so the implications of these issues were briefly discussed.