The aim of the present research is to propose a spectral method for solving optimal control problem indirectly using Boubaker - Turki polynomial functions as basis functions. To achieve this goal, explicit representation formulas for some interesting operational matrices for Boubaker - Turki polynomials functions are first derived which play an important role in dealing with the problem of optimal control. They are operational matrix of derivative, operational matrix of product. By applying the obtained operational matrices and spectral scheme, the main problem is transformed to a set of linear algebraic equations that greatly simplifies the problem. The presented method in details by solving numerical example has been investigated. A new recursive relation of the Boubaker - Turki and Chebyshev polynomials of the second kind as well as a general formula for power function as a linear combination of the Boubaker - Turki polynomial are also included in this work.