Data depth has been applied as a nonparametric measurement for ranking multivariate samples. In this talk, we focus on homogeneity tests to assess whether two multivariate samples are from the same distribution. There are many data depth-based tests for this problem, but they may not be very powerful, or have unknown asymptotic distributions, or have slow convergence rates to asymptotic distributions. Given the recent development of data depth as an important measure in quality assurance, we propose two new test statistics for multivariate two-sample homogeneity tests. The proposed test statistics have simple asymptotic half-normal distribution and chi-squared distribution with degree of freedom one. We also discuss the generalization of the proposed tests to multiple samples. The simulation study demonstrates the superior performance of the proposed tests. The test procedure is illustrated by two real data examples.