In this work, the realistic performance analysis of low earth orbit (LEO) satellite communication network is performed in terms of coverage probability in the communication scenario which includes stochastic geometry-based modeling of LEO satellites and gateways (GWs). The positions of LEO satellites and GWs are modeled with Binomial point process and Poisson point process, respectively. The realistic coverage performance results of interference-limited LEO satellite communication systems are obtained under the interference effect. Thus, the performance analysis of LEO satellite communication network is carried out in a more realistic way. Also, the extensive simulation results are examined in terms of various system parameters including the number of satellites, the number of available channels and GW density.