Construction project cost control is an important aspect of project management. This paper aims to provide an effective cost control management mode for the construction industry by studying the application of big data technology in cost prediction and control management of construction projects. The standard particle swarm algorithm is optimized by establishing a particle object element model, performing iterative and hierarchical updating of particles, and introducing the Tent mapping strategy. Then it is used in the optimization of the Extreme Learning Machine algorithm to design a construction project cost prediction and control model based on APSO-LLM. The index system of the construction project cost prediction and control model is constructed, and the convergence effect, prediction effect, and case application of the model are analyzed. The APSO-LLM model enhances the convergence speed and search accuracy, boosts the optimal fitness by 0.037, and maintains a construction cost prediction error below 3%. The study proves the APSO-LLM model’s applicability, accuracy, and good prediction effect in cost prediction and construction project control.