In this paper we introduce a new channel model for modeling land mobile satellite channels through the implementation of $\kappa-\mu$ based shadowed Rice model. This model characterizes the amplitude of the direct signal using the $\kappa-\mu$ distribution and offers mathematically straightforward expressions for essential channel statistics, such as the envelope probability density function (PDF), the moment generating function (MGF) of the instant power, and the outage probability (OP). The model is beneficial in examining and forecasting the behavior of narrowband and wideband land mobile satellite systems and can be utilized for various uncoded/coded modulations and diversity arrangements. Results of comparison with existing channel data demonstrate the model’s proficiency in precisely depicting a broad range of channel conditions and propagation processes over satellite links, while also offering a more efficient computational method in comparison to other established models.