The effort invested in a software project is one of the most challenging task and most analyzed variables in recent years in the process of project management. Software cost estimation predicts the amount of effort and development time required to build a software system. It is one of the most critical tasks and it helps the software industries to effectively manage their software development process. There are a number of cost estimation models. Each of these models have their own pros and cons in estimating the development cost and effort. This paper investigates the use of Back-Propagation neural networks for software cost estimation. The model is designed in such a manner that accommodates the widely used COCOMO model and improves its performance. It deals effectively with imprecise and uncertain input and enhances the reliability of software cost estimates. The model is tested using three publicly available software development datasets.The test results from the trained neural network are compared with that of the COCOMO model. From the experimental results, it was concluded that using the proposed neural network model the accuracy of cost estimation can be improved and the estimated cost can be very close to the actual cost.