To achieve a high-speed adaptive filter by using a BLMS algorithm.

The adaptive filter includes L sets of system which are respectively provided with delay devices 21...2(k-1)...2(L-1) for delaying an input signal 1 in many stages, P-pieces of first multipliers for respectively multiplying P-kinds of delay device output signals in the delay devices by P-kinds of filter coefficients 70, an adder for adding the whole results of P-pieces of multiplications to obtain an output signal, a second multiplier for multiplying a difference between the output signal 80k and a desired signal 50k by a step size, and P-pieces of third multiplier for respectively multiplying the results of the multiplications by the P-kinds of delay device output signals. The filter coefficient of a succeeding block is obtained from the multiplication results and the filter coefficients and, then, the filter coefficients 70 are updated.