This paper addresses a model for statistical simulation of narrow-band dual polarized Multi input Multi output (MIMO) land mobile satellite (LMS) channel for low earth orbit (LEO) satellites. It considers the change of the satellites elevations and hand over from one satellite to another during the same communication session. It introduces a detailed description and block diagrams to generate the time series signals with the desired power, probability distribution, covariance relations and spectrum. The simulation results are useful for the design of MIMOLMS data communication systems.