In addition to the spectral redshift of galaxies, the prediction of galaxies redshift has important research significance for studying the large-scale structure and evolution of the universe. In this paper, we use the metering and spectral data of 150 000 galaxies of SDSS DR13 released by the Sloan Sky Survey project to analyze the galaxies according to the color characteristics and clustering methods. The classification results show that the early galaxies account for a large proportion. In this paper, three different machine learning algorithms are compared to measure the redshift regression prediction of early galaxies and find the optimal method. In the experiment, the photometric values of the galaxy samples u, g, r, i, z and the 10 color features obtained by the difference between the two bands are used as input data. First, the BP network is constructed, and the BP algorithm is used to measure the galaxies redshift. Then the Genetic Algorithm (GA) is used to optimize the parameters of the BP network, and the optimized GA-BP algorithm is applied to the regression prediction experiment of the early galaxies; considering the complex operation of the GA algorithm will affect the prediction efficiency. Moreover, the Particle Swarm Optimization algorithm not only has high stability and simple operation, so the Particle Swarm Optimization algorithm is used to optimize the BP network (PSO-BP) and Particle Swarm Optimization is used to optimize BP network (PSO-BP). By adjusting the weight method to improve the prediction efficiency and increase the stability, the particle swarm optimization algorithm is used to predict the redshift of the early galaxies in the galaxy samples. In the experiment, the spectral redshift is taken as the expected value, and the mean square error (MSE) is used as the error analysis index to judge the accuracy of the three algorithms. The PSO-BP regression prediction results are compared with the BP network model and the GA-BP network model. The experimental results show that the MSE value of the BP network is 0001 92, the MSE value of the GA-BP network is 0001 728, and the MSE value of the PSO-BP network is 0001 708. The experimental results show that the PSO-BP optimization model used in this paper is superior to the BP neural network model and the GA-BP neural network model in terms of accuracy, which is respectively improved by 111% and 12%. It is superior to the traditional K-nearest neighbor test in efficiency, which overcomes the shortcomings of traversing all data samples in KNN algorithm and its generalization performance is better than that of other BP network optimization models.