Abstarct: The main goal of this thesis is to introduce the hesitant fuzzy simplex method for solving hesitant fuzzy linear programming problems, for this purpose we first introduce different states of hesitant fuzzy linear programming problems. first state, linear programming problems where only the coefficients of the fuzzy objective function are hesitant fuzzy numbers. the second case, linear programming problems where the decision variables and values on the right side are ‎hesitant‎ fuzzy numbers. The third case, linear programming problems where all coefficients and variables are hesitant fuzzy.‎ Then we state the hesitant fuzzy simplex method for each of the states and proved the optimality theorems, then present the initial hesitant fuzzy simplex algorithm.‎ Finally, we present and solve practical examples for each case. The introduced hesitant fuzzy simplex method preserves the information of the problem until the end of the solution steps, and also the optimal solutions remain in the hesitant fuzzy space.