In this paper, linear quadratic optial control probles are solved by applying least square method based on Bézier control points. We divide the interval which includes t, into k subintervals and approximate the trajectory and control functions by Bézier curves. We have chosen the Bézier curves as piacewise polynomials of degree three, and determined Bézier curves on any subinterval by four control points. By using least square ethod, e introduce an optimization problem and compute the control points by solving this optimization problem. Numerical experiments are presented to illustrate the proposed method.