This paper proposes an innovative algorithm for forecasting the motion response of floating offshore wind turbines by employing force-to-motion transfer functions and state-space models. Traditional numerical integration techniques, such as the Newmark-β method, frequently struggle with inefficiencies due to the heavy computational demands of convolution integrals in the Cummins equation. Our new method tackles these challenges by converting the problem into a system output calculation, thereby eliminating convolutions and potentially enhancing computational efficiency. The procedure begins with the estimation of force-to-motion transfer functions derived from the hydrostatic and hydrodynamic characteristics of the wind turbine. These transfer functions are then utilized to construct state-space models, which compactly represent the system dynamics. Motion responses resulting from initial conditions and wave forces are calculated using these state-space models, leveraging their poles and residues. We validated the proposed method by comparing its calculated responses to those obtained via the Newmark-β method. Initial tests on a single-degree-of-freedom (SDOF) system demonstrated that our algorithm accurately predicts motion responses. Further validation involved a numerical model of a spar-type floating offshore wind turbine, showing high accuracy in predicting responses to both regular and irregular wave conditions, closely aligning with results from conventional methods. Additionally, we assessed the efficiency of our algorithm over various simulation durations, confirming its superior performance compared to traditional time-domain methods. This efficiency is particularly advantageous for long-duration simulations. The proposed approach provides a robust and efficient alternative for predicting motion responses in floating offshore wind turbines, combining high accuracy with improved computational performance. It represents a promising tool for enhancing the development and evaluation of offshore wind energy systems.