The invention provides a compressor control circuit of a fixed-frequency air conditioner and the fixed-frequency air conditioner. When a compressor is operated, an access control unit in a filter module is controlled to be connected with an inductor in the filter module in parallel by a control module after the compressor is started, the inductor is controlled to access to a power supply loop of the compressor, and harmonic waves which are generated after the compressor is started are filtered, so that the problem of abnormal start of the compressor due to low working voltage of the loading compressor because partial pressure is generated by the inductor when the inductor accesses to the power supply loop of the compressor after the compressor is started is solved, and the reliability of the compressor control circuit is increased.