To address the defects of the salp swarm algorithm (SSA) such as the slow convergence speed and ease of falling into a local minimum, a new salp swarm algorithm combining chaotic mapping and decay factor is proposed and combined with back propagation (BP) neural network to achieve an effective prediction of tool wear. Firstly, the chaotic mapping is used to enhance the formation of the population, which facilitates the iterative search and reduces the trapping in the local optimum; secondly, the decay factor is introduced to improve the update of the followers so that the followers can be updated adaptively with the iterations, and the theoretical analysis and validation of the improved SSA are carried out using benchmark test functions. Finally, the improved SSA with a strong optimization capability to solve BP neural networks for the optimal values of hyperparameters is used. The validity of this is verified by using the actual tool wear data set. The test results of the benchmark test function show that the algorithm presented has a better convergence speed and solution accuracy. Meanwhile, compared with the original algorithm, the R² value of the part life prediction model proposed is improved from 0.962 to 0.989, the MSE value is reduced from the original 34.4 to 9.36, which is a 72% improvement compared with the original algorithm, and a better prediction capability is obtained.