Fully coupled time-domain simulation is essential for the analysis and design of floating wind turbines (FWTs); however, its high computational cost remains a bottleneck for large-scale parametric and optimization studies. Conventional integrators such as the fourth-order Runge–Kutta (RK4) method require multiple force evaluations per time step; this increases the runtime in aero–hydro–servo–elastic models. To overcome this limitation, a predictor–corrector one-force (PC-1F) time-integration scheme was developed using the in-house simulation tool, Pywind. This scheme enforced a single synchronized force evaluation per time step while preserving second-order accuracy and eliminating empirical damping. PC-1F was verified against RK4 on the IEA 15 MW semisubmersible FWT under wind-only, wave-only, and coupled load cases. Results showed that PC-1F strongly agreed with RK4, exhibiting correlation coefficients above 0.95, mean discrepancies within 0.5% for key response quantities, and consistent power spectral densities in the wave-frequency band (0.05–0.3 Hz). Efficiency tests demonstrated that PC-1F achieved 70%–90% higher iteration rates than RK4, confirming its comparable fidelity at substantially reduced cost. These findings establish PC-1F as a practical, engineering-ready alternative to multistage integration schemes. It can also be employed for accelerated parametric sweep studies and uncertainty quantification and integrated into multiobjective optimization frameworks for next-generation FWT design.