As a version of the optimum block adaptive (OBA) algorithm, a nested optimum block adaptive (NOBA) algorithm is proposed for finite impulse response (FIR) block adaptive filters. In this paper, we introduce a new updating procedure called the nested iteration technique that updates the filter tap weights several times rather than only once for each data block, as in the OBA algorithm. Thus; the proposed algorithm achieves faster convergence speed although its computational load is higher than the OBA algorithm. The NOBA algorithm is formulated by minimizing an estimate of the block mean-square error (BMSE) as an objective function. Through computer simulations, it is shown that the proposed algorithm is superior to the normalized least mean-square (NLMS) algorithm in convergence rate regardless of stationarity, whereas the OBA algorithm is inferior to the NLMS algorithm. It is also shown that the tracking property of the NOBA algorithm is better than that of the OBA algorithm, and it is almost comparable to that of the NLMS algorithm.