Based on discrete element method，a heterogeneous model considering the crystal size distribution was established by combining the grain-based model and parallel-bonded stress corrosion model. Through the comparative analysis of laboratory test and numerical simulation results，the applicability and reliability of the method of creep mechanical properties of granite were verified，and it is revealed that the heterogeneity caused by the crystal size distribution has significant influence on creep failure time，steady creep rate，number of microcracks and long-term strength. The main research conclusions are as follows：(1) The smaller the heterogeneity index，the more homogeneous the rock is，and the higher the uniaxial compressive strength and long-term strength are. The ratio of the long-term strength to the uniaxial compressive strength is about 0.70. (2) Under the same stress，the larger the heterogeneity index，the smaller the creep failure time is. Under the same driving stress ratio，the creep rate of the rock decreases and the creep failure time increases with increasing the heterogeneity index. (3) The development of microcracks is roughly divided into three stages including slow expansion，constant velocity expansion and accelerated expansion. The number of intergranular tensile microcracks is most and then intragranular tensile microcracks，followed by intergranular shear microcrack. (4) The microstructure of rock plays a controlling role in failure mode，and microcracks are preferred in the process of expansion. When the model is homogeneous，the failure mode exhibits cleft breakage. when the heterogeneity increases，the failure mode transforms to shear failure. The expansion of microcracks originates from crystal grain boundary with an obvious“bypassing core”phenomenon，that is，the feldspar with larger grain size has obvious influence on microcrack propagation and failure mode. The larger the rock heterogeneity，the more obvious the phenomenon is.