Abstract: Considering the spread spectrum problem of finite-control-set model predictive control (FCS-MPC), a Model predictive control technique for the quasi Y-Source Inverter with RL load to enhance the following effectiveness of the tracking efficiency by using the cost function. The controller achieves optimal voltage vector by minimizing the errors in one cost function, the weighting factor for each absolute error has been used, the system has been tested under dynamic load change, and fast response has been achieved using FCS- MPC for the output load current. Moreover, the controller maintains capacitor voltage to be constant with no minimum value over/under-shoot. The MPC model has been created and then the whole system has been validated under MPC based on MATLAB SIMULINK Software. The results of output currents, capacitors voltages, and inductor current have been presented and detailed discussed The results show how fast the MPC is in tracking the reference signal.