There exist numerous sophisticated models and methods for estimating the size, cost and schedule of software projects. However, the ability to accurately predict the software cost of web based software for agile software projects is still dubious. The most appropriate web based software cost estimation in an agile software development environment is a big problem due to varying levels of customer requirement and different individual personnel capabilities. Also, the need to develop a separate model to estimate web based project is rising. In this research paper, we present AgileMOW, an approach to model a software cost estimation process which will evaluate effort and cost of software development for web based projects developed using Agile methodology with a number of constraints imposed by stakeholders and environmental characteristics, thereby satisfying multitudinous criteria by making use of COCOMO II model, a famous traditional algorithmic technique. Most importantly, the paper identifies the difference between conventional and web projects. The proposed estimation model enhances the level of visibility in the planning stages.