Network meta-analysis (NMA) is gaining popularity in evidence synthesis and network meta-regression allows us to incorporate potentially important covariates into network meta-analysis. In this article, we propose a Bayesian network meta-regression hierarchical model and assume a general multivariate t distribution for the random treatment effects. The multivariate t distribution is desired for heavy-tailed random effects and converges to the multivariate normal distribution when the degrees of freedom go to infinity. Moreover, in NMA, some treatments are compared only in a single study. To overcome such sparsity, we propose a log-linear regression model for the variances of the random effects and incorporate aggregate covariates into modeling the variance components. We develop a Markov chain Monte Carlo sampling algorithm to sample from the posterior distribution via the collapsed Gibbs technique. We further use the deviance information criterion and the logarithm of the pseudo-marginal likelihood for model comparison. A simulation study is conducted and a detailed analysis from our motivating case study is carried out to further demonstrate the proposed methodology.