By the merits of hierarchial orthogonal polynomial, a method of constructing a class of orthogonal-reinforced hierarchical hexahedra vector finite elements(ORHHVFE) to achieve a better condition of systematic matrix is presented, and the basis functions of hierarchical hexahedra vector finite elements(HHVFE) at the angle of conforming elemental systematic matrices are studied in detail. Numerical tests of the ORHHVFE constructed using 1-st Legendre polynomials based on the above method and the other HHVFE were carried out and compared. The results show that the ORHHVFE has the same numerical precision with the HHVFE, and the conditions of systematic matrices by the ORHHVFE are improved largely.