In this paper, laser-induced breakdown spectroscopy (LIBS) was used to obtain 320 sets of spectral data at different positions on the surfaces of aluminum alloy samples. Then, these spectral data were preprocessed, and 20 characteristic spectral lines of the six main elements in aluminum alloy were selected to form a 320×20 spectral data matrix. Next, the 20 variables that were inputted into the model were reduced to 6 through principal component analysis. Finally, the reduced-dimensional spectral data were inputted into the radial basis function neural network model to establish multivariate calibration models for five main nonaluminum elements (Si, Fe, Cu, Mn, and Mg) in aluminum alloy. The results revealed that the mean goodness of fit of the model was 0.978 and its mean root mean square error was 0.31%. Principal component analysis combined with a radial basis function neural network can effectively reduce parameter fluctuations, correct matrix effects, and improve the accuracy and stability of the model quantitative analysis; in particular, this combination can significantly improve the accuracy of analysis of elements with relatively low content, such as Fe, Si, and Cu.