Ground motion is often broken down into two horizontal components (x, y) and one vertical component (z). In order to explore the feasibility of the application of Copula model in the correlation analysis of multi-dimensional ground motion parameters, 1 500 sets of measured ground motions were selected from the Pacific Engineering Seismic Research Center and 12 groups of ground motion parameters were selected from intensity, duration and spectrum to characterize and analyze the correlation between different directional components of ground motion. Firstly, Pearson linear correlation coefficients, Kendall rank correlation coefficients and Spearman rank correlation coefficients of 12 groups of ground motion parameters in the u-v (u and v are any two components of two horizontal components and one vertical component of ground motion, u, v = x, y, z) direction were calculated. Secondly, the optimal probability models of 12 groups of ground motion parameters in x-direction, y-direction and z-direction were established based on Kolmogorov-Smirnov (K-S) test and the Bayesian information criteria (BIC). Finally, the optimal Copula function of ground motion parameters between u-v components was determined by BIC criterion, and the joint probability function of 12 groups of ground motion parameters between u-v components was established. The results show that the correlation of ground motion parameters in the 12 groups is good, but the correlation of peak response spectrum corresponding period parameters in the u-v direction and the correlation of arias intensity parameters in the x-z direction and y-z direction is low. The joint probability function of ground motion parameters between u-v direction components can be established accurately by Copula theory. Given the ground motion parameters of u-direction component, the Copula conditional mean and conditional random number obtained can be used to predict the ground motion parameters of v-direction component.