Introduction: Prior studies have shown that parent-adolescent relationships and peer relationships may be important factors associated with adolescent mobile phone addiction (MPA). The present study aims to further explore the direct effects of parent-adolescent and peer relationships on adolescent MPA as well as the indirect effects through the mediating roles of autonomy, competence, and relatedness needs satisfaction. Methods: Our sample consisted of 1766 Chinese adolescents (53.10% male; M = 13.33, SD = 1.94, range from 10 to 18 years) who completed questionnaires regarding parent–adolescent relationships, peer relationships, psychological needs satisfaction, and MPA. SPSS 24.0 was used to analyze correlations among variables and Mplus 7.4 was used to test the structural equation model in this study. Results: (1) positive parent-adolescent relationships were negatively associated with adolescent MPA, while peer relationships did not show a significant association with MPA; (2) autonomy and competence needs satisfaction significantly mediated the effects of parent-adolescent and peer relationships on MPA, while the mediating role of relatedness need satisfaction between parent-adolescent and peer relationships and MPA was not significant; (3) the mediating effect of competence need satisfaction between peer relationships and MPA was significantly stronger than that between parent-adolescent relationships and MPA. Conclusions: This study explored the different mechanisms by which parent-adolescent and peer relationships influence adolescent MPA. These discoveries may contribute to intervention and prevention programs for adolescent MPA.