An accurate, complete and realistic channel model is required to accurately analyze the system performance of a multiple input multiple output (MIMO) broadband satellite mobile communication system with dual-orthogonal polarized antennas (DPAs). In most current studies, the channel characteristic matrix (CCM) is always formed by an independent identical distribution (i.i.d) model of Rayleigh or Rice distribution and nevertheless incomplete and inaccurate to describe a broadband dual-orthogonal polarized MIMO land mobile satellite (BDM-LMS) channel. This paper focuses on establishing the BDM-LMS channel statistical model, which combines the 4-state broadband LMS channel model, the time selective fading features, the channel covariance information (CCI) channel model and polarization correlations between antennas. The modeling steps of the channel model are introduced. The main emphasis is placed on the effects of the factors, such as antenna numbers, temporal correlations, terminal environments, elevation angles and polarization correlations between the DPAs, on the channel capacity in the BDM-LMS system. Many simulation results are provided to illustrate the effects of these factors through comparisons of the transmit rate, ergodic capacity and outage capacity with different factor values. Besides, the MIMO outage capacity advantages, which indicate the benefits of MIMO compared with a single input single output (SISO) system under the same channel condition, are also studied under i.i.d or BDM-LMS channel.