An intelligent integral backstepping sliding mode control (IIBSMC) system using a multi-input multi-output (MIMO) recurrent neural network (RNN) is proposed to control the position of a levitated object of a magnetic levitation system considering the uncertainties in this study. First, the dynamic model of the magnetic levitation system is derived. Then, an integral backstepping sliding mode control (IBSMC) system with an integral action is proposed for the tracking of the reference trajectory. Moreover, to relax the requirements of the needed bounds and discard the switching function in IBSMC, an IIBSMC system using a MIMO RNN estimator is proposed to improve the control performance and further increase the robustness of the magnetic levitation system. The adaptive learning algorithms are derived using Lyapunov stability theorem to train the parameters of the RNN online. Finally, some experimental results of the tracking of periodic sinusoidal trajectory demonstrate the validity of the proposed IIBSMC system for practical applications.