Tukey's method provided simultaneous inference for all-pairwise comparisons (MCA) under balanced design, usual normality and equality of variances assumptions. Under the unbalanced design, the Tukey-Kramer method assumes the variances are equal across all treatment groups. It provides a set of conservative simultaneous confidence intervals for all-pairwise differences and has been widely used. In practice, however, homogeneity of variances is seldom satisfied. In this article, an approximate approach is proposed when the equality of variances cannot be assumed and the ratios of population variances among treatments are known from previous experience. The results from a simulation study show that the error rate of the Tukey-Kramer method is excessive, while the error rate of the proposed method is within the nominal level when the variances are different. In addition, an approximate approach is proposed to provide the simultaneous confidence intervals for all-pairwise differences when the ratios of variances are unknown.