Abstract: In this paper, a method of empirical orthogonal expansion for a vector field is proposed. The vector values at N×T points form a N×T matrix. We can find the vector empirical orthogonal functions which approximate each column of the matrix more accurately in the Iight of root mean square error. This can be done by solving a complex eigen-value problem. There are N empirical orthogonal functions for a matrix of N columns. The meteorological vector field may be expanded into its empirical orthogonal functions. Examples of such vector expansion are given in this paper. It has been clearly shown that better results can be obtained by vector expanison as compared with ordinary scalar expansion.