As part of the rock mass, the non-persistent joints inherently affect the rock mass mechanical behavior. Nearly most of the existing calculation methods of the rock mass damage variable can only consider the influence of the joint geometrical property on its mechanical behavior. Therefore, this study focuses on the mechanical behavior of the rock mass with a set of non-persistent joints in order to propose a new calculation method of the rock mass damage variable which can both consider the influence of the joint geometrical and mechanical properties on the rock mass mechanical behavior. First, the hypothesis of elastic complementary energy equivalence is adopted to replace the Lemaitre strain equivalence hypothesis in order to study the anisotropic damage of the rock mass induced by the joints. And based on the connection of the increment of additional strain energy caused by the existence of one joint in fracture mechanics and the emission of damaged strain energy in damage mechanics, the calculation formula of the rock mass damage variable caused by one joint is deduced. Second, the calculation formula of the stress intensity factor(SIF) KⅠ and KⅡ of a single joint tip under uniaxial compression is studied according to the fracture mechanics theory. Third, the calculation formula of SIF KⅠ and KⅡ of a set of one or more-rowed joint tips is given by considering the interaction among the joints. Finally, the calculation formula of the rock mass damage variable caused by a set of non-persistent joints is obtained; and then its validity is verified by the existing test results.