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In this paper, we consider a feasible primal–dual interior point method for linear semidefinite programming problem ( S D P ) based on Alizadeh–Haeberly–Overton ( AHO ) direction (Monteiro, 1997). Firstly, and by a new and simple technique, we establish the existence and uniqueness of optimal solution of the perturbed problem ( S D P ) μ and its convergence to optimal solution of ( S D P ) . Next, we present new different alternatives to calculate the displacement step. After, we establish the convergence of the obtained algorithm and we show that its complexity is O ( n ln [ ε − 1 ( 〈 X 0 , S 0 〉 ) ] ) . Finally, we present some numerical simulations which show the effectiveness of the algorithm developed in this work. [ABSTRACT FROM AUTHOR]