The purpose of this study was to investigate the PISA2003 database by Hierarchical Linear Model (HLM). This plan of PISA2003 aimed at the evaluation of mathematics and problem-solving ability. The sample included 41 nations, and the task-takers participating in PISA2003 were high school students whose age was about 15-year-olds.There will be estimation errors if all the task-takers were put in the same level when it went to analyze all the casual relation between the variables of nations and students. Therefore, HLM of two levels was used to analyze the PISA2003 database. The unit in level-1 was students. The variables belonging to the level-1 were score of mathematics cognition and mathematics confidence. As to the level-2, the unit was nations and the variable was GCI (Growth Competitiveness Index). The results of HLM analysis showed that the GCI can explain the variance of mathematics cognition for each nation separately. Moreover, the higher this variable was, the higher mathematics cognition will be. Finally, based on the findings of this study, some suggestions for future research were provided.