The increasing availability of computing power in the past two decades has been used to develop new techniques for optimizing the solution of estimation problem. Today's computational capacity and the widespread availability of computers have enabled the development of a new generation of intelligent computing techniques, such as the algorithm of our interest. This paper presents a new member of the class of stochastic search algorithms (known as Canonical Genetic Algorithm "CGA") for optimizing the maximum likelihood function ln (L(θ, σa2 )) of the first order moving average MA(1) model. The presented strategy is composed of three main steps: recombination, mutation, and selection. The experimental design is based on simulating the CGA with different values of (θ), and sample size n. The results are compared with those of moment method. Based on MSE value obtained from both methods, one can conclude that CGA can give estimators (\hat \theta) for MA(1) parameter which are good and more reliable than those estimators obtained by moment method.