The multiparameter eigenvalue problem originates from the theory of canonical correlation analysis, which is used to analyze the correlation between multiple sets of variables. The canonical correlation analysis is one of the important methods of multivariate statistics, and has a wide range of applications in econometrics, biostatistics and signal processing. The extrapolation Jacobi method is used to solve two kinds of multiparameter eigenvalue problems and the convergence of this method is proved. The effectiveness of the extrapolated Jacobi method is illustrated by numerical examples, and it is compared with the classical Jacobi method, Gauss-Seidel method and SOR method.