This paper uses an orthogonal collocation-based parametrization of control variables and the sequential quadratic programming (SQP) optimization technique to calculate a space shuttle’s re-entry trajectory. Re-entry trajectory design is crucial and challenging due to non-linear entry dynamics, the vehicle’s lack of propulsion, boundary conditions, and the need to adhere to these limitations properly. Finding the best possible control profiles, including bank angle and angle of attack, to produce the best possible re-entry trajectory is crucial to resolve this problem successfully. Both these control profiles are parametrized using Chebyshev collocation method. Three re-entry mission objectives are considered, including maximization of cross-range, minimization of maximum peak heat rate, and minimization of total heat, to demonstrate that this approach results in a re-entry trajectory. Further, the optimal value of decision variables is obtained using sequential quadratic programming method to achieve mentioned re-entry mission objectives. Simulation results demonstrate that the optimal re-entry trajectories generated using this parametrization method have accurately satisfied the mission objectives and terminal constraints.