The paper presents application of direct pseudospectral Chebyshev method for solving a commercial airplane trajectory optimization problem. This method employs Nth-degree Lagrange polynomial approximations for the state and control variables with the values of these variables at the Chebyshev-Gauss-Lobatto (CGL) points as the expansion coefficients. This process is converted to a nonlinear programming problem (NLP) with the state and control values at the CGL points as unknown NLP parameters. The kinetic model of flight is formulated, where it is assumed that an airplane is a particle and the motion takes place in the vertical plane. The method is implemented in Matlab using sequential quadratic programming algorithm (SQP) as an efficient solver. Sensitivity analyses are performed concerning the influence of the degree of discretization and the initial approximation on the solution. Three examples of optimized trajectories in presence of wind are shown.