Hydraulic fracturing technology is an effective way to develop tight sandstone reservoirs with low porosity and permeability. The tight sandstone reservoir is heterogeneous and the heterogeneity characteristics has an important influence on fracture propagation. To investigate hydraulic fracture performance in heterogeneous tight reservoir, the X-ray diffraction experiments are carried out, the Weibull distribution method and finite element method are applied to establish the uniaxial compression model and the hydraulic fracture propagation model of heterogeneous tight sandstone. Meanwhile, the sensitivity of different heterogeneity characterization factors and the multi-fracture propagation mechanism during hydraulic fracture propagation is analyzed. The results indicate that the pressure transfer in the heterogeneous reservoir is non-uniform, showing a multi-point initiation fracture mode. For different heterogeneity characterization factors, the heterogeneity characteristics based on elastic modulus are the most sensitive. The multi-fracture propagation of heterogeneous tight sandstone reservoir is different from that of homogeneous reservoir, the fracture propagation morphology is more complex. With the increase of stress difference, the fracture propagation length increases. With the increase of injection rate, the fracture propagation length increases. With the increase of cluster spacing, the propagation length of multiple fractures tends to propagate evenly. This study clarifies the influence of heterogeneity on fracture propagation and provides some guidance for fracturing optimization of tight sandstone reservoirs.