Let A be a  quaternion matrix,  be the standard eigenvalues of A,    be the minimal polynomial of A. The quaternion similarity orbit of the quaternion matrix A is defined as the set    is any invertible  quaternion matrix}. In this paper, we show that the norm closure of  is the set  is the  quaternion matrix:  for all  where  denotes the rank of quaternion matrix T,  is a monic polynomial with real coefficients,  denotes  dividing  

quaternion matrix, quaternion similarity orbit, minimal polynomial, rank.