This paper presents a new frequency-domain adaptive algorithm for sparse echo cancellation by incorporating a sparse partial (SP) subblock selection scheme into the multi-delay filtering (MDF) algorithm. Unlike the sparse partial tap selection method, the proposed algorithm selects the active regions based on FFT subblocks such that frequency bins within each subblock can be updated evenly. Simulation results show that the proposed algorithm has faster convergence performance with same steady-state mean squared error (MSE) as existing sparse partial MDF algorithms based on tap selection.