The inductance parameter is crucial in realizing high precision model predictive control for a grid-connected inverter. The traditional inductance identification method is easily affected by grid frequency deviation and cannot be used when the active power is zero. To improve the frequency robustness of the inductance parameter in model predictive control, an online identification method based on MRAS is proposed. First, a second-order sliding mode observer is designed to observe the grid voltage. Second, without compensating for the observed voltage amplitude and phase deviation caused by the low-pass filter, the actual grid voltage also generates the same amplitude and phase deviation. Then, using the relationship between the voltage and inductance errors, an inductance identification model is established to overcome the impact of grid frequency deviation on the results, and the identification is also available when the active power is zero. Finally, by incorporating the identified parameter into the model predictive control algorithm, the control of the inverter can be more accurate. The effectiveness and accuracy of the proposed method is verified by experiment.