Abstract: For the data from multivariate t distribution, it is hard to do influence analysis based on its probability density function. But it can be considered as a particular Gaussian mixture by introducing the weight from the Gamma distribution. Based on this fact, we treat the weight as the missing data and develop the local influence analysis for the data from multivariate t distribution based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. The local influence based on the case-weights perturbation is discussed in detail and two numerical examples are given to illustrate our results.