An FIR filter and setting method of filter coefficients thereof enabling the prevention of breakdown of equi-ripple of weighted approximation error and preservation of gain of the pass band into approximately constant. The setting method includes five steps. The initial setting step is that setting of the FIR filter, setting of the band, setting of coefficients of a pre-filter, and setting of initial extreme value point. The first step is that interpolation polynomial equation is generated for interpolating amplitude characteristic from the present extreme value point of the amplitude characteristic of the frequency. The second step is that a new extreme value point is determined from the amplitude characteristic obtained from the interpolation polynomial equation that is obtained in the first step. The third step is that judgement is performed whether or not position of the extreme value is approximated within required range while repeating the first step and the second step. The fourth step is that finding of the filter coefficients is performed from the approximated amplitude characteristic obtained in the third step.