We discuss the problem of shrinkage estimation for the autocovariance matrix of a Gaussian stationary vector-valued process to improve on the usual sample autocovariance matrix with respect to the mean squares error. We propose a kind of empirical Bayes estimators when the mean of the stochastic process is zero and non-zero. \cl{We show that the shrinkage estimators dominate the usual estimators, and the asymptotic risk differences are similar to that of scalar-valued Gaussian stationary processes. This result seems to be useful for the autocovariance estimation with vector-valued dependent observations.}