A programmable gain amplifier comprises: an operational amplifier, N (N>0) attenuation capacitances, N+1 group of control capacitance modules, multiple change-over switches, a change-over control module and a feedback switch. Each group of control capacitance module has at least one control capacitance. Each change-over switch is controlled by the change-over control module, the common ends of the switches are respectively connected with the second end of the control capacitances, the capacitances, by said connection, are connected with an input signal, a reference voltage, or the output end of the operational amplifier. The feedback amplifier connects between the output end and No.1 input end of the operational amplifier, it is getting-through at No.1 phase period, and cutting-off at other period. At No.2 phase period, the control capacitance can be connected, controlled by the change-over switch, the output end of the operational amplifier to be used as feedback capacitance.