The statistical analysis often failed to work when the zero elements are reported in the compositional data. To overcome the problem, we first construct a framework for analyzing the compositional data with zero entries by introducing a stochastic representation. Furthermore, we propose a new distribution, called the Dirichlet Composition Distribution, by assuming the base vector follow independent Gamma distributions. We discuss the Dirichlet Composition Distribution in detail, including its moments, the calculation of MLEs via EM algorithm and the regression model, etc. The simulation results have shown the performance of our proposed model is satisfactory. Finally, our method is employed to analyze the data of fluorescence in situ hybridization (FISH) for chromosome detection. The proportions of zero entries, the parameters of base vectors and regression coefficients are presented to analyze the data.