The grid-connected converter (GCC) is widely used as the interface between various distributed generations and the utility grid. To achieve precise power control for GCC, this paper presents a model predictive direct power control (MPDPC) with consideration of the unbalanced filter inductance and grid conditions. First, the characteristics of GCC with unbalanced filter inductance are analyzed and a modified voltage control function is derived. On this basis, to compensate for the power oscillation caused by unbalanced filter inductance, a novel power compensation method is proposed for MPDPC to eliminate the DC-side current ripple while maintaining sinusoidal grid current. Besides, to improve the control robustness against mismatched filter inductance, a filter inductance identification scheme is proposed. Through this scheme, the estimated value of filter inductance is updated in each control period and applied in the proposed MPDPC. Finally, simulation results in PSCAD/EMTDC confirm the validity of the proposed MPDPC and the filter inductance identification scheme.