Adaptive algorithm based on multi-channel linear prediction (MCLP) is an effective dereverberation method. However, the abrupt change of the target speech source position makes it difficult to guarantee both the fast convergence speed and the optimal steady-state behavior. In this letter, the recursive-least-squares (RLS)-based and Kalman-filter-based adaptive MCLP method for speech dereverberation are investigated. Based on the relative weighted change of the adaptive filter coefficients, a time-varying forgetting factor for the RLS algorithm and a re-initialization mechanism for the Kalman filter are proposed to make the algorithm robust to the abrupt change of the target speaker positions. The advantages of the proposed scheme are demonstrated in the experiments.