Software cost estimation is an important phase in software development. It predicts the amount of effort and development time required to build a software system. It is one of the most critical tasks and an accurate estimate provides a strong base to the development procedure. In this paper, the most widely used software cost estimation model, the Constructive Cost Model (COCOMO) is discussed. The model is implemented with the help of artificial neural networks and trained using the perceptron learning algorithm. The COCOMO dataset is used to train and to test the network. The test results from the trained neural network are compared with that of the COCOMO model. The aim of our research is to enhance the estimation accuracy of the COCOMO model by introducing the artificial neural networks to it.