A day-ahead dispatch model for microgrids under source-load uncertainty conditions is established to enhance their economical effectiveness. In view of the source-load uncertainty composed of photovoltaic power and demand, a novel adaptive optimization decision-based distributionally robust optimization is proposed to overcome the conservativeness of traditional robust optimization. Firstly, a conservativeness-adjustable ambiguous set of source-load uncertainty is constructed, which can flexibly adjust the conservatism through distribution constraints. Meanwhile, auxiliary uncertainty variables are introduced to transform the ambiguous set into a manageable form. Secondly, leveraging the duality principle of infinite programming and fixing the dual variables, the distribution uncertainty is reduced to scenario uncertainty. Finally, employing an extreme dual variable generation method, the proposed model is converted into a deterministic programming in a two-stage solving framework. Numerical simulations verify the superiority of the proposed model in balancing the economical effectiveness and robustness of microgrid operations.