The wake field, impedance and output signal for SSRF BPM have been calculated and analyzed by using the numerical simulation code of MAFIA. The narrow-band impedance of BPM arising from formation of resonance in its cavity like structure either is harmful to beam or limits the performance of BPM itself, and should be reduced to tolerable levels. The calculated results show that there are three main peaks in the impedance spectrum of the SSRF BPM prototype, and two of which are above the limit. After lots of simulations for different shapes of the BPM button, a new structure of SSRF BPM have been found, and there is only one main peak, which is under the limit, in the impedance spectrum. Its output signal also meets the requirement.