This research presented latent growth models of general happiness and school happiness among Taiwanese high school students. The relationships of these two types of happiness and academic competence were also examined. Seven hypotheses were made based on the economic and psychological explanations of happiness, the academic emotion theory, the broad-and-build theory, and the theory of eudaimonic well-being. The data from the Taiwan Educational Panel Survey were analyzed, and latent growth modeling and cross-lagged correlation were conducted. First, it was found that high school students showed decreasing general happiness and school happiness as grade level increased. However, there were slower declines for those with higher initial levels of general happiness. Second, the cross-lagged correlations showed that general happiness and school happiness significantly predicted each other. These findings implied that the economic explanation would better explain the origin of happiness than the psychological explanation. Third, the relationship between general happiness and academic competence was not significant. Fourth, the higher the initial level of school happiness, the slower the academic competence grew. The growth slope of academic competence was correlated positively with the growth slope of school happiness. But the growth slope of school happiness was negatire. Students with faster growth of academic competence would experience faster decline of school happiness. It implied that academic competency might grow at the cost of decreasing school happiness. These findings did not support the prediction from the academic emotion theory, broad-and-build theory, or theory of eudaimonic well-being. However, the theories of academic emotion and eudaimonic well-being were supported by results from the cross-lagged correlations. It showed that school happiness in Grade 7 positively predicted academic competency in Grade 9, which in turn predicted school happiness in Grade 11. It suggested that in the same educational stage, school happiness affected academic competence; while transitioning between two educational stages, academic competency affected the following school happiness. Further research and practical implications were discussed.