A bandpass sigma-delta modulator with the function of adjustable center-frequency is present in this paper. A method used to convert 2-order low-pass modulator to 4-order bandpass modulator is proposed to realize the design. Center-frequency that can be set to 1/6, 1/4 and 1/3 of sampling frequency is controlled according to the digital logic voltage. The bandwidth of pass-band is 200 Hz. Test results show that the average SNR is about 80 dB at different center-frequency when the sampling frequency is 64 kHz. The input signal can reach to −3 dBFs. The complexity to design a variable center-frequency bandpass modulator is greatly reduced.