The Recursive Least Square algorithm optimization method used in this paper for the synthesis of antenna array radiation pattern in adaptive beam forming. In this paper optimum value of weights of each antenna element is determined which produces radiation pattern with minimum side lobe level. Optimization is done using 8-elements array with an optimum interelement spacing to avoid grating lobes. Simulation is done in MATLAB and can be taken into consideration, to obtain the desired beam inthe lookup direction.