ABSTRACT Let be the real algebra of all n-square quaternion matrices. Moreover, let . In this paper, the notion of C-numerical range of n-square quaternion matrices is introduced. Some algebraic and geometrical properties of them are investigated. In particular, a necessary and sufficient condition for the convexity of C-numerical range of a quaternion matrix is given, where C is a real matrix. Moreover, C-numerical radius of quaternion matrices is introduced.