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The present paper proves chaos phenomenon for a range of parameters in attitude dynamic of a satellite and designs an appropriate nonlinear controller, while ensuring optimal system performance, the controller guarantees control of a chaotic state. As the dynamic equations of a three-axis satellite are defined as a nonlinear non-autonomous system, a technique is offered for calculating the Lyapunov exponents of such systems that may express the system’s chaotic state. Using the technique, the chaotic behavior of a system is proved within a range of parameters. Then a back-stepping sliding mode controller is proposed based on the desired performance and the closed-loop system stability is proved based on the Lyapunov’s theorem. Moreover, converting the system into a compatible form with the conditions of the Melnikov theorem using this analytical method ensures removing chaos phenomenon in the controlled system. Calculating Lyapunov exponents of the closed system confirms this issue. Finally, the simulation results obtained from the proposed controlling actions for different work fields are presented.