The global damage index of frame is defined as the loss of the strain energy dissipation capability during the pushover process, and the local damage index of plastic hinge is defined as the loss of hysteretic energy dissipation capability during the pushover process. Based on the force analogy method, the analytical expressions of the global local damage index are proposed. Besides, the correlation between global damage index and local damage indexes are discussed. The results show that improving hysteretic energy dissipation capability and constraint capacity to elastic portion of plastic hinges will effectively improve the strain energy dissipation capability of frame. There are three specific ways:reducing strength degradation, residual deformation and improving rotation capacity of plastic hinges. The global damage index is generally closed to weighted value of local damage indexes which taking the ratio of hysteretic energy dissipated by plastic hinge to total value dissipated by frame as weight. Therefore, the weighted value of local damage indexes could be used to estimate the global damage index of structure.