The aim of this paper is to estimate probability distribution functions with maximum entropy and known quantiles. The paper formulates the problem as a nonlinear optimization problem, and converts it into a system of nonlinear equations by Lagrange multipliers method. Finally, an efficient method is proposed to obtain a solution of the nonlinear system. The method needs to solve a linear programming problem in each iteration. Since linear programming problems can be solved in a reasonable time, our proposed method is faster than generic methods of solving nonlinear programming problems. Several computational experiment are provided to demonstrate the performance and validation of our proposed method.