Multivariate meta-analysis has been established as useful tools for synthesizing exsiting clinical trials evidence with multiple outcomes, e.g., meta-analysis for diagnostic studies, network meta-analysis. Although ordinary likelihood-based methods or Bayesian analyses with non-informative priors have been adopted for the inference in multivariate random effects models, validities of these methods are founded on large sample theory. As widely known in conventional univariate meta-analyses, coverage probabilities of confidence intervals of these methods can be substantially below the target level (e.g., Brockwell and Gordon, Statist Med 2007, 26: 4531-43), and it generally follows in multivariate models. One of effective approaches to resolve this serious problem is adopting improved methods based on higher order asymptotics. In this study, we develop the Bartlett-type correction method for the efficient score statistic of multivariate random effects models. We can develop an improved confidence interval using the modified efficient score statistic, and it can be straightforwardly extended to multivariate meta-regression. We evaluate its practical effectiveness via simulations.