Two-dimensional (2D) membranes are emerging candidates for osmotic energy conversion. However, the trade-off between ion selectivity and conductivity remains the key bottleneck. Here we demonstrate a fully crystalline imine-based 2D polymer (2DPI) membrane capable of combining excellent ionic conductivity and high selectivity for osmotic energy conversion. The 2DPI can preferentially transport cations with Na⁺ selectivity coefficient of 0.98 (Na⁺/Cl⁻ selectivity ratio ~84) and K⁺ selectivity coefficient of 0.93 (K⁺/Cl⁻ ratio ~29). Moreover, the nanometer-scale thickness (~70 nm) generates a substantially high ionic flux, contributing to a record power density of up to ~53 W m⁻², which is superior to most of nanoporous 2D membranes (0.8~35 W m⁻²). Density functional theory unveils that the oxygen and imine nitrogen can both function as the active sites depending on the ionization state of hydroxyl groups, and the enhanced interaction of Na⁺ versus K⁺ with 2DPI plays a significant role in directing the ion selectivity.