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In this paper, the joint mean-covariance estimation problem is considered under the scenario that the number of samples is small relative to the problem dimension. The samples are assumed drawn independently from a heavy-tailed distribution of the elliptical family, which can model scenarios where the commonly adopted Gaussian assumption is violated either because of the data generating process or the contamination of outliers. Under the assumption that prior knowledge of the mean and covariance matrix is available, we propose a regularized estimator defined as the minimizer of a penalized loss function, which combines the prior information and the information provided by the samples. The loss function is chosen to be the negative log-likelihood function of the Cauchy distribution as a conservative representative of heavy-tailed distributions, and the penalty term is constructed with the prior being its global …