The received signal in Rician multipath channels is modeled as a complex constant, accounting for the main line-of-sight (LoS) path, added to a circular complex Gaussian random variable, modeling all the diffusive secondary paths. The Rician K-factor is accordingly defined as the ratio between the powers of LoS and diffusive components. Under this (widely assumed) multipath model, a closed-form expression for the Rician K-factor estimate is commonly obtained exploiting the second and fourth moments of the received signal amplitude. However, in mobile communications, random shadowing effects make the LoS component fluctuating (Rician shadowed model) leading to a performance degradation of the conventional estimator. With focus on land mobile satellite communications, in this letter, a novel estimation procedure of the Rician K-factor, aimed at avoiding the bias error of the conventional estimator when the LoS component is Nakagami-m distributed, is proposed and assessed. Specifically, the estimate is computed using the solution of a system of three equations and three unknowns in conjunction with the likelihood function of the received signal. The performance analysis shows that the new estimator can guarantee better performance than the conventional estimator.