Model predictive control is a powerful methodology that involves repeatedly solving an optimization problem over a moving time horizon, using predictions of the system’s future behavior and response. Model predictive control is especially useful for handling model and parameter uncertainty in real-world applications, and it has become a wide-spread solution methodology in industry. Typically, the nonlinear system dynamics are approximated by linearized dynamics and the controller, which is designed based on the linear system, is used to control the nonlinear system. This approach requires solution of the Riccati equation. The key contribution of this thesis is the development of a model predictive controller, that operates directly on the nonlinear system dynamics, for optimal spacecraft attitude control. This developed controller incorporates Chebyshev Picard methods (CPM) to solve the model predictive control (MPC) of the spacecraft attitude dynamics. The optimal control formulation leads to a boundary value problem where the initial costates must be iterated to solve for the optimal control that drives the system to the desired final attitude. A unique formulation of the Chebyshev-Picard boundary value solver is implemented, whereby the state and costate equations are simultaneously integrated forward and backwards respectively over the finite receding horizon. Simulation results are presented for an attitude maneuver using the new algorithm which allows for a comparison of its performance to that of the classical Linear Quadratic Regulator, as well as a shooting method that utilizes MATLAB’s fsolve and ode78. Low and high-fidelity simulations are performed in which the high-fidelity simulations include the effects of external disturbances that produce torques on the spacecraft. CPM-MPC is able to handle the disturbances due to Earth’s gravity gradient, atmospheric drag, magnetic field as well as solar radiation pressure without any convergence issues.