In this thesis, a new multivariate zero-inflated double Poisson distribution is proposed, which is considered as the generalization of univariate zero-inflated double Poisson distribution. The statistical properties of new distribution, such as joint probability mass function, expectation, covariance matrix, marginal distribution and conditional distribution, are derived. The maximum likelihood estimates of parameters are obtained. The score test statistic is derived to test zero inflation of multivariate count data with many zeros by using score function and information matrix. The empirical powers of score test are gained by a simulation study. The application of real data is performed to test zero inflation.