The development of floating offshore wind turbines (FOWTs) is gradually moving into deeper offshore areas with more harsh environmental loads, and the corresponding structure response should be paid attention to. Safety assessments need to be conducted based on the evaluation of the long-term extreme response under operating conditions. However, the full long-term analysis method (FLTA) recommended by the design code for evaluating extreme response statistics requires significant computational costs. In the present study, a power response prediction method for FOWT based on an artificial neural network algorithm is proposed. FOWT size, structure, and training algorithms from various artificial neural network models to determine optimal network parameters are investigated. A publicly available, high-quality operational dataset is used and processed by the Inverse First Order Reliability Method (IFORM), which significantly reduces simulation time by selecting operating conditions and directly yielding extreme response statistics. Then sensitivity analysis is done regarding the number of neurons and validation check values. Finally, the alternative dataset is used to validate the model. Results show that the proposed neural network model is able to accurately predict the extreme response statistics of FOWT under realistic in situ operating conditions. A proper balance was achieved between prediction accuracy, computational costs, and the robustness of the model.