With the wide application of quaternion, the solution of large quaternion structured matrix equations has become an important topic in scientific computing. Based on the new positive definite and skew-self-conjugate splitting iteration (NPSS), two new mixed-parameter splitting iteration schemes were constructed for the quaternion sub-positive definite system AX = B by introducing the two-parameter and relaxation acceleration techniques. That is, asymmetric new positive definite and skew-self-conjugate splitting (ANPSS), successive over relaxation asymmetric new positive definite and skew-self-conjugate splitting (SANPSS), and the convergence of these two iterations was proved by using the eigenvalue theory of quaternion matrix, and the range of relevant parameters was given. In addition, the complex representation method of quaternion matrix was used to realize the numerical solution of the system in MATLAB environment. Numerical examples show that the flexible selection of multiple parameters shows that the proposed mixed parameter splitting iteration has higher convergence efficiency than NPSS iteration.