Improving the mechanical performance of low-carbon offshore steel is of great significance in shipbuilding applications. In this paper, a new Cu-Cr microalloyed offshore structural steel (FH36) was developed based on EH36. The microstructure, mechanical properties, and fatigue crack propagation properties of rolled plates of FH36, EH36, and normalizing rolled EH36 plates (EH36N) manufactured by a thermo-mechanical control process (TMCP) were analyzed and compared (to simplify, the two rolled specimens are signified by FH36T and EH36T, respectively). FH36T showed an obvious advantage in elongation with the value of 29%, 52.2% higher than the EH36T plates. The normalizing process led to a relatively lower yield stress (338 MPa), but substantially increased the elongation (33%) and lessened the yield ratio from 0.77 to 0.67. Electron back-scattered diffraction (EBSD) analysis showed that SFs of the deformation texture of FH36T and EH36N along the transverse direction (TD) and normal direction (ND) were much higher than those of the EH36T plate, which enhanced the lateral movement ability in the width and thickness direction, enhancing the ductility. Moreover, FH36 plates showed a better fatigue crack propagation resistance than rolled EH36 plates. The formation of the jagged shape grain boundaries is believed to induce a decrease of effective stress intensity factor during the fatigue crack propagation process.