We propose a scheme to enhance photon blockades simultaneously in two microwave cavities connected by a giant atom. In the case that only one cavity is weakly driven, we observe that the enhanced photon blockades occur in both cavities at the same time, which is attributed to the anharmonic eigenenergy spectrum constructed by the resonantly coupled giant atom. When the cavity and the atom are simultaneously driven, the stronger photon blockades in two cavities can be successfully achieved by the destructive quantum interference of two-photon excitation. Interestingly, we find that high single-photon occupations can be obtained in both cases. Moreover, we give the optimal conditions for conventional and unconventional photon blockades through analytical calculations, which are in good agreement with numerical results. Our scheme opens a prospective path to achieve simultaneous photon blockades in two indirectly coupled cavities, and provides a promising method to generate the high-quality and brightness single photon source.