This research demonstrates a model of a wind energy conversion system that operates at different wind speed, with results simulated in MATLAB SIMULINK. The wind turbine system is made up of three parts or subsystems namely the aerodynamic, mechanical and electrical blocks. The system is designed by modeling differential equations for each block and then simulated in SIMULINK environment. The Squirrel Case Induction Generator, horizontal axis wind turbine system with complexities of all three parts of the wind turbine model were analyzed using the mathematical equations, with each block modeled and designed separately, then all three blocks joined together to give the complete unit. Wind speed data from Ogoja community in southern part of Nigeria was used to test the simulation performance. The system simulation was tested and worked satisfactorily, with different wind speed giving proportionate mechanical torque and turbine speed. This model therefore demonstrates that wind energy could be extracted in the region even at varying wind speed.