Low Earth orbit (LEO) satellites are becoming an increasingly promising solution for enhancing maritime communications and introducing a new avenue for signal transmissions from shore-to-ship. The traditional performance modeling for satellite networks based on a grid of circular orbit geometries does not apply to large-scale LEO satellite communication networks, limiting analytical insights. To address this issue, this paper proposes a tractable theoretical framework for an LEO satellite-aided shore-to-ship communication network (LEO-SSCN) that models the distribution of LEO satellites as a binomial point process (BPP) uniformly distributed around the Earth. The framework aims to obtain the end-to-end signal transmission performance by considering signal transmissions from the network service center to the destination ship via either a marine link or a space link, which is subject to Rician or Shadowed Rician fading, respectively. Since the distance from the serving satellite to the destination ship is intractable, we first propose a distance approximation approach. Then, based on the approximation, we employ stochastic geometry to derive the analytical expressions of the end-to-end transmission success probability as a function of the Laplace transform from interfering satellites’ power. Numerical results verify the accuracy of our analysis. This framework paves the way for more reliable integration of the LEO satellites and the existing maritime communication network.