In this letter, we propose a frequency-weighted block LMS (FWBLMS) algorithm that is based on minimization of the frequency-weighted block mean-squared error. The FWBLMS algorithm has an important advantage over the rime-domain LMS algorithm in that it can be designed with different frequency-weighting on error signal depending on the relative significance of various frequency bands. Application of the FWBLMS algorithm in adaptive near prediction of speech is discussed.