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Software companies develop different software in parallel, which is a very complex task. Project managers have to manage different software development processes based on different time, cost, and number of staff, sequentially. Software time, cost, and number of staff estimates are the critical tasks for project managers in software companies. Estimation of these parameters at early stage of software project planning is one the challenging issued in software project management, for the last decade. Software cost and time estimation supports the project planning and tracking, and it controls the expenses of software development. Software effort estimation refers to the estimates of the likely amount of cost, schedule, and manpower required to develop a software. Accurate effort estimate at the early phase of software development can help project managers to efficiently control project progress and improve the project success rate. This paper proposes a novel artificial neural network (ANN) prediction model incorporates Constructive Cost Model (COCOMO), ANN-COCOMO II, to provide more accurate software estimates at the early phase of software development. This model uses the advantages of artificial neural networks such as learning ability and good interpretability, while maintaining the merits of the COCOMO model. The ANN is utilised to calibrate the software attributes using past project data, in order to produce accurate software estimates. The proposed model is evaluated using 156 sets of project data from two data sets, COCOMO I and NASA93. The analysis of the obtained results shows 8.36% improvement in estimation accuracy in the ANN-COCOMO II model, when compared with the original COCOMO II.