Mass function is used to handle uncertainty. Quaternion number is the extent of imaginary number. In this paper, the classical mass function is extended by quaternion number, named as Quaternion Mass Function (QMF). The proposed QMF has the advantage to deal with uncertain information. When the quaternion number degenerates into the complex number, then the QMF degenerates into the complex mass function. In addition, if the complex mass function is degenerated as real number, the QMF is the same as mass function in classical evidence theory. In the case when the quaternion number degenerates into the real number and the QMF focus on the frame of discernment with single subsets, the QMF is the same as the probability distribution in probability theory. The combination rule is also presented to combine two QMFs, which is the generalization of Dempster rule. In the case when the quaternion mass function degenerates into the real number and assigns only to single subsets, the proposed combination rule is degenerated as Beyesian updation in probability theory. Numerical examples are applied to prove the efficiency of the proposed model. The experimental results show that the proposed model can apply the quaternion theory to mass function effectively and successfully.