Due to no dc-link energy storage element in the matrix converter (MC), its input and output performances are highly sensitive to the unbalanced grid conditions. In order to mitigate the adverse effects of the unbalanced grid voltages, this paper proposes a simple and effective control strategy based on the finite-control set model predictive control (FCS-MPC). In this case, an extended instantaneous power theory is adapted to generate the source current references. As a result, both sinusoidal source currents and balanced output currents are ensured. Besides, complicated positive and negative sequence decomposition is avoided. Furthermore, an extended state observer (ESO) is designed to eliminate the grid voltages sensors, which not only estimates the grid voltages but also provides the delayed grid voltage information required for the source current reference calculation. The effectiveness of the proposed method is verified by the simulation and experimental results.