The eigenvalue and the singular value of a quatemion matrix play important roles in the applications of quaternion matrix theory. By virtue of the blocked matrix and the corresponding identities, several inequalities on the eigenvalue and the singular value of quaternion matrices are established, which generalize the corresponding results existing in the real or the complex matrix theory. The results of this paper may help to improve the applications of quaternion algebra in such related fields as quantum mechanics, robot technology and the like.