Handwritten Devanagari script recognition system using neural network is presented in this paper. Diagonal based feature extraction is used for extracting features of the handwritten Devanagari script. After that these feature of each character image is converted into chromosome bit string of length 378. More than 1000 sample is used for training and testing purpose in this proposed work. It is attempted to use the power of genetic algorithm to recognize the character. In step-I preprocessing on the character image, then image suitable for feature extraction as here is used. Diagonal based feature extraction method to extract 54 features to each character. In the next step character recognize image in which extracted feature in converted into Chromosome bit string of size 378. In recognition step using fitness function in which find the Chromosome difference between unknown character and Chromosome which are store in data base.