This research was intended to clearly describe the differences in mathematical problem-solving abilities about initial mathematical abilities by applying the Problem-Based Learning and Discovery learning models. The research design employed a quantitative approach. The sample of this research was students of SMA Negeri 1 Mamosalato, Grade XI MIA 1, as the first and second experiment classes were XI MIA 2. This research applied an experimental method with a factorial design of 2 x 3. The instrument was administered to collect data to test initial mathematic ability and mathematical problem-solving abilities—data was analyzed in two ways: ANOVA and Tukey test (LSD test). The findings of the research were (1) there were differences in mathematical problem-solving abilities by applying the Problem-based Learning Model and Discovery Learning Model, (2) there was no interaction between the learning model and initial mathematical abilities on mathematical problem-solving abilities, (3) there was difference in students mathematical problem-solving abilities by applying Problem-based Learning Model and Discovery learning Model, especially to high initial mathematical abilities, middle initial mathematical abilities, as well as low initial mathematical abilities.