Software cost estimation involves the estimation of cost required to develop a software. Cost overrun, schedule overrun occur in the software development due to the wrong estimate made during the initial stage of software development. So proper estimation is very essential for successful completion of software development. Lot of estimation techniques available to estimate the effort in which neural network based estimation method play a prominent role. ELMAN neural network a recurrent type network can be used to estimate the cost. For a good predictor system the difference between estimated cost and actual cost should be as low as possible. To control better the time, cost and resource assigned to software project, organization need proper estimate of their size even before the project actually start. The development of a software system is an inherently complex process Estimating the cost needed to run a large software development project is doubly so and notoriously difficult.