Many scholars who study in social mobility have observed that the social status of the father does influence their children on how they will gain their social status in the future; however, it is the education those children receive that strongly influences their status in society. As the government proceeds with the policy of "Go South" and grants people the permission of visiting their relatives that dwell in Mainland China, an unrest wave of cross-border marriage was thus brought up. At the moment, it has been the time that the second generation of these cross- border marriages enters school and begins their compulsory education. According to several scholars' observation, these people who are cross- borderly engaged receive lower social status; therefore, the issue that whether their children would confront difficulties when they receive education has obviously become a fervent topic of public affairs. Accordingly, this study aims to investigate the children of the newly immigrant brides who have been in the elementary schools of Peng-hu County in the school year of 2003. In this research, the family background of the students is independent variable while the students¡¦ self-adaptation in elementary school is a dependent variable. How these variables influence one another are discussed in this study in order to figure out whether these children of newly immigrant brides confront any specific difficulties if they are facing problems in their learning at schools. Questionnaires were distributed for the empinical data, and the results were examined through descriptives, t-test,ANOVA and chi-square test, and after which, further inference and calculations were made. The findings of the study show as follow: 1. The school performance, learning attitude and the self-adaptation of the children of newly immigrant brides in Peng-hu County does not fall behind those of native children. This result differs to the general perceptions that the adaptation of these children from newly immigrant brides can not catch up with other native children. 2. The families of these newly immigrant brides in Peng-hu tend to be with low social and economical status. 3. The children whose mother come from Mainland China embrace better performance in language learning than native children, especially in learning ¡§Chinese spelling alphabets¡¨ and ¡§oral speaking competence.¡¨ However, no significant differences were found among these children in learning mathematics . 4. A mother¡¦s Mandarin ability influences her children¡¦s academic performance. 5. The writing ability of children of newly immigrant brides in Peng-hu County depends on the proportion between teacher and student at school. Suggestion: It is the first time we face the issue that the second generation of these cross- border marriages begin their education in school in Taiwan. If the survey could be directed and made by the Ministry of Education, different results come from differednt region study and different approaches could possibly be avoided, and the wrong decision making could also be prevented.