Offshore floating wind turbines (OFWTs) are expected as the future of wind energy. However, the analysis of OFWTs is much more complicated than that of fixed-bottom wind turbines. The simulators currently in use, based on the classic blade element momentum (BEM) theory, will be inadequate while used on OFWTs because of the unsteady motions induced by wind and waves. Thus, simulators with advanced approaches are of necessity for analyzing OFWTs. In this work, a coupled aero-hydrodynamic simulator in MATLAB/Simulink is developed, for simulating the response and aerodynamic performance of OFWTs under wind and waves in the time domain. For aerodynamics, the code uses an unsteady BEM model or the free vortex wake method (FVM) to calculate the aerodynamic loads and performance of the wind turbine. For hydrodynamics, a linearized classic marine hydrodynamic model, based on the frequency-dependent parameters obtained from the code of WAMIT, is employed to calculate the hydrodynamic loads of the platform by solving the hydrostatic, diffraction and radiation problems with fluid-memory effect. Furthermore, Morison's equation and the strip theory are applied to calculate the nonlinear viscous drag for improving the quality of the model. Finally, a series of cases with different wind and wave conditions is tested on a sample model combining "NREL offshore 5-MW baseline wind turbine" with "OC3-Hywind platform". The results show that the simulator is able to predict the response and aerodynamic performance of OFWTs under wind and waves. Moreover, the FVM is more suitable for analyzing the aerodynamic performance of OFWTs than the unsteady BEM model because of its higher fidelity and less limitations.