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The aim of this paper is to automatically compose new pleasing music from randomly generated notes without human intervention. To achieve this goal, Genetic Algorithm was implemented to generate random notes. The Neural Network was trained on a set of melodies to learn their regularity of patterns and then it is used as a fitness evaluator for the generated music from the Genetic Algorithm. Four Genetic Algorithms (using different combinations of tournament, roulette-wheel selections and one-point, two-point crossovers) were used in generating music to compare them according to which one is the most suitable for music composition. The experiments show that using tournament selection and two-point crossover produces better music patterns than using other combinations by 57%. The experiments show that the generated music was good and the results were promising. For evaluation, 10 music experts were asked to listen and evaluate four samples of the generated music; two of them were evaluated high from the Neural Network and two were evaluated low. Then we compared their results with the results from the Neural Network. The results show that the error rate for Neural Network was 16.7% and accuracy was 83.3%.