Optical nonreciprocity and nonreciprocal devices such as optical diodes have broad and promising applications in various fields, ranging from optical communication to signal process. Here, we propose a magnet-free nonreciprocal scheme based on the four-wave mixing (FWM) effect in semiconductor quantum dots (SQDs). Via controlling the directions of the coupling fields, the probe field can achieve high transmission in the forward direction within a certain frequency range due to the FWM effect. And the transmission of the probe field in the backward direction undergoes significant reduction, as the FWM effect is absent. The calculation results show a wide nonreciprocal transmission window with isolation greater than 12 dB and insertion loss lower than 0.08 dB. The influences of the Rabi frequencies of the coupling fields, the medium length, and the decay rates on the nonreciprocal propagation of the probe field are also studied, showing the requirements of these parameters for good nonreciprocal performances. Our work may offer an insight for developing optical nonreciprocal devices based on the FWM process and the SQD system.