Software effort and cost estimation are crucial parts of software project development. It determines the budget, time, and resources needed to develop a software project. The success of a software project development depends mainly on the accuracy of software effort and cost estimation. A poor estimation will impact the result, which worsens the project management. Various software effort estimation model has been introduced to resolve this problem. COnstructive COst MOdel (COCOMO) is a well-established software project estimation model; however, it lacks accuracy in effort and cost estimation, especially for current projects. Inaccuracy and complexity in the estimated effort have made it difficult to efficiently and effectively develop software, affecting the schedule, cost, and uncertain estimation directly. In this paper, Particle Swarm Optimization (PSO) is proposed as a metaheuristics optimization method to hybrid with three traditional state-of-art techniques such as Support Vector Machine (SVM), Linear Regression (LR), and Random Forest (RF) for optimizing the parameters of COCOMO models. The proposed approach is applied to the NASA software project dataset downloaded from the promise repository. Comparing the proposed approach has been made with the three traditional algorithms; however, the obtained results confirm low accuracy before hybrid with PSO. Overall, the results showed that PSOSVM on the NASA software project dataset could improve effort estimation accuracy and outperform other models.