Software cost estimation is the measurement of the effort and resource required to develop a software system for a particular defined time period. From the last few years, many software cost estimation models have been proposed for the estimation of effort and development time. The cost of the software can be estimated easily in the mid of project development. But with further study, we found that the cost must be estimated before the start of the project, to satisfy customer as well as developer's needs. In earlier proposed cost estimation models, cost estimation is done with more than 20 parameters at the early conceptual phase and if input is not defined using logical approach, then the results of estimation are unpredictable. This paper presents simple approach for estimating software development effort with a minimum set of parameters yet sufficient, that can be easily identified at an early stage while considering all possible aspects. We also introduced a weight factor in the estimation of effort for improving the accuracy of the estimation and the proposed weight factor is calculated by expert learning system. Further, we developed a web based tool for the estimation of cost based on our proposed approach. Finally, we compare our result with previous works on early estimation and conclude with the points of accuracy that we observe while comparing the results with existing approaches.