The finite-cover element-free method FCEFM is applied to simulate the fracture and damage evolution process of geo-materials. This method is mathematically based on the finite-cover technique of manifold method and the multiple weighted moving least-square method to solve the continuous and discontinuous problems without meshing or re-meshing. The damage heterogeneity and evolutionary processes of rock mass with initial cracks are analyzed and numerically simulated by FCEFM. Using the method of probability to generate the parameters of materials randomly, the physical and mechanical properties of materials are randomly distributed in nodes or Gaussian points. And an alternating damage model together with numerical implementation which is adapted to microscopic elasto-brittle fracture analysis is proposed. Through analysis of several numerical examples, the validity and efficiency of progressive fracture analysis with use of the proposed FCEFM is demonstrated.