This paper describes the implementation of a genetic algorithm to evolve the population of weight matrices for storing and recalling the patterns in a Hopfield type neural network model. In the Hopfield type neural network of associative memory, the appropriate arrangement of synaptic weights provides an associative function in the network. The energy function associated with the stable state of this model represents the appropriate storage of the input patterns. The aim is to obtain the optimal weight matrix for efficient recall of any prototype input pattern. For this, we explore the population generation technique (mutation and elitism), crossover and the fitness evaluation function for generating the new population of the weight matrices. This process continues until the selection of the last weight matrix or matrices has been performed. The experiments incorporate a neural network trained with multiple numbers of patterns using the Hebbian learning rule. In most cases, the recalling of patterns using a genetic algorithm seems to give better results than the conventional recalling with the Hebbian rule. The simulated results suggest that the genetic algorithm is the better searching technique for recalling noisy prototype input patterns.