Hydraulic fracturing is a key technique for developing unconventional reservoirs. Affected by the stress shadow and heterogeneity, the fractures propagate unevenly, which obviously restricts the production rate. To date, the limited-entry and non-uniform perforation techniques are commonly used to promote multi-fracture even growth. In this study, an efficient planar 3D fracture simulator is developed to study the propagation of multiple fractures during horizontal well fracturing. The simulator considers stress interaction and fluid distribution among clusters. Using the model, a series of numerical simulations are conducted to investigate the multi-fracture propagation with non-uniform perforation. First, we estimate the value of stress interaction for different fractures based on the approximate solution of PKN fracture in the viscosity-dominated regime, and improve the dimensionless parameter that characterizes the competition between stress interaction and perforation friction. The fluid distributes evenly when the perforation friction is larger than stress interference. And then, a method to design non-uniform perforation is proposed. Results show that: when the in-stage stress is homogeneous, the perforation parameters should be selected under the condition that the perforation friction is larger than stress interference. When the in-stage stress is heterogeneous, based on the perforation parameters selected under the homogeneous stress conditions, increase perforation holes in the high stress cluster and make the reduction of perforation friction equal to the value of the in-stage stress heterogeneity, as a result, the stress heterogeneity can be balanced by decreasing the perforation friction of the high-stress clusters. A series of simulations show that the proposed method is efficient and make satisfactory results for a practical case. The results can be helpful for non-uniform perforation designing for multiple fractures fracturing in a horizontal well.