Motivated by a real data analysis, we in this paper propose a new multivariate t (MVT) distribution via stochastic representation instead of the joint density function. This new distribution is called Type II MVT distribution, which possesses several remarkable features including (1) all components follow univariate t-distributions with different degrees of freedom, (2) it could include components following the multivariate normal distributions when the corresponding degrees of freedom approach to infinity, and (3) it could contain independent/uncorrelated components. Because of avoiding three drawbacks associated with the traditional MVT distribution, this new distribution is more flexible in model specification and applicable to any high-dimensional data. Important distributional properties are explored and useful statistical methods are developed. Simulation studies are performed to evaluate the proposed methods. Two biomedical data sets are used to compare the proposed Type II MVT distribution with the traditional MVT distribution.