Abstarct: Abstract A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. A suitable scalarization technique is employed for the multi-objective optimal control problem. By using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. Then, we present a numerical procedure for solving optimal control problems with both linear terminal constraints and multiple criteria. Using a Chebyshev spectral procedure, the problem reduces to a constrained optimization problem which can be solved using hybrid penalty partial quadratic interpolation technique. In the end, combine the optimal control method Discrete Mechanics and Optimal Control with reference point techniques to compute Pareto optimal control solutions.