Due to the irregularity features of finite mixture model, classic inference procedures are usually not directly applicable. Many testing procedures have been studied for testing for homogeneity though only a few of them are concerning mixture with multi-dimensional parameter kernel density. We develop a framework for testing homogeneity based on the profile Likelihood ratio. The proposed test statistic has a nice and simple asymptotic distribution, mixture of Chi squares. Penalties on mixing proportion and model parameters are introduced to control type I error while preserving the power. The result is applicable for mixture models with general multi-dimensional parameter kernel densities. Specifically, mixture of Gamma distribution and mixture of Logistic distribution are studied in detail. Simulations are conducted to assess the size and power of the test.