In this study, we discuss a multiple comparison procedure with a control for multivariate one-sided test in each pairwise comparison. For pairwise comparisons, we use the approximate likelihood ratio test statistics derived by Tang et al. (An approximate likelihood ratio test for a normal mean vector with nonnegative components with application to clinical trials. Biometrika 1989, 76, 577–583). We derive a formula to determine the critical value for pairwise comparisons satisfying a specified significance level. Furthermore, we formulate the power of the test for our multiple comparison procedure. Finally, we give some numerical examples regarding the critical values and the power of the test.