The existing damage ratio strength theory using the damage ratio variable is only applicable for concrete, and the deviatoric traces are concave for high hydrostatic pressures. To expand the theory’s application scope and make up for the deficiency, this paper proposes a six-parameter expression of the damage ratio variable considering the effect of both the Lode angle and the hydrostatic pressure. The values of the variable obtained by the proposed expression are verified by the experimental stress-strain curves of concrete under uniaxial, biaxial, and triaxial stress states. The modified criterion for concrete using the six-parameter damage ratio variable better represents the corresponding characteristics of the failure surface compared to the previous one. The proposed criterion is compared to the experimental data, against some strength criteria, which confirm the validity of the proposed criterion for concrete and lightweight aggregate concrete. Furthermore, for biaxial stress states, simplified criterion curves are also proposed.