In almost all adaptive dereverberation algorithms based on the multi-channel linear prediction (MCLP) model, it is assumed that the filter length can cover the reverberation time. However, in many practical situations, a deficient length filter, whose length is less than the reverberation time, is employed in consideration of computational cost. A deficient length filter fails to fully model the late reverberation, resulting in degraded performance. In this paper, we present a new MCLP-based adaptive dereverberation algorithm to improve the dereverberation performance when using a deficient length filter. We introduce a gain and use the filter coefficients estimated from the previous frame to track the MCLP modeling errors of the current frame. The gain and the filter coeffi-cients are jointly optimized and solved by using an alternating minimization technique. Experimental results show the superiority of the proposed algorithm. The shorter the filter length is, the more advantageous the proposed algorithm is.