Software effort estimation is the process of predicting the number of human required to develop a particular software project. During software development, the initial requirement is usually changed and this makes the project manager to update the software effort, cost, and schedule. To manage the change of effort, cost, and schedule of a software project, the initial software effort, and cost estimation need to be accurate. Various researchers have used machine learning algorithms and algorithmic techniques to improve the accuracy of software effort estimation. The Constructive Cost Model (COCOMO) is an algorithmic model which is widely used as a software effort, cost, and time estimation model. However, the COCOMO model and machine learning-based approach have limitation on estimating the software effort accurately due to the non-deterministic nature of the problem. Meta-heuristic algorithms are better to find near-optimum solutions at a reasonable computational cost for parameter optimization. So that it can be a good technique. In this research paper, a hybrid genetic and particle swarm optimization algorithm based model is proposed. A hybrid genetic and particle swarm optimization algorithm is used for optimizing the coefficient parameters of intermediate COCOMO model. The thesis used the strength of the two algorithms to design an effective software effort estimation model. PSO used to generate an initial local optimum solution and GA used to optimize parameter values of COCOMO coefficients. The proposed model was trained and tested using NASA software datasets. To evaluate the performance of our model, we used the five well known and widely used software effort and cost estimation accuracy measures: - Percentage of Prediction (PRED (0.25)), Magnitude Relative Error (MRE), Mean Magnitude Relative error (MMRE), Mean of absolute error (MAE), and Mean absolute percentage error (MAPE). The results showed that the Magnitude relative error (MRE) of the proposed model in comparison with COCOMO, GA, and PSO model is reduced to 362.07%, 120.53%and 21.81% respectively.