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In software engineering, the planning and budgeting stages of a software project are of great importance to all stakeholders, including project managers as well as clients. The estimated costs and scheduling time needed to develop any software project before and/or during startup form the basis of a project's success. The main objective of soft- ware estimation techniques is to determine the actual effort and/or time required for project development. The use of machine learning methods to address the estimation problem has, in general, proven remarkably successful for many engineering problems. In this study, a fully connected neural network (FCNN) model and a metaheuristic, gray wolf optimizer (GWO), called GWO-FC, is proposed to tackle the software development effort estimation (SEE) problem. The GWO is integrated with FCNN to optimize the FCNN parameters in order to enhance the accuracy of the obtained results by improving the FCNN's ability to explore the parameter search field and avoid falling into local optima. The proposed technique was evaluated utilizing various benchmark SEE datasets. Furthermore, various recent algorithms from the literature were employed to verify the GWO-FC performance. In terms of accuracy, comparative outcomes reveal that the GWO-FC performs better than other methods in most datasets and evaluation criteria. Experimental outcomes reveal the strong potential of the GWO-FC method to achieve reliable estimation results. [ABSTRACT FROM AUTHOR]