Demand response (DR) has significant potential in optimizing power resource allocation and alleviating grid stress, attracting growing attention in power system. However, the price-based demand response (PDR) real-time electricity pricing strategy tend to ignore the back-and-forth correlation of multi-moment customer electricity consumption, fail to reflect the trend of electricity price changes, and the centralized real-time pricing (RTP) strategy are prone to leaking customer privacy. To resolve these limitations, we propose a multi-stage Markov-based distributed privacy-preserving framework for RTP under smart grid. Initially, we consider the bidirectional influence between the electricity provider and users, propose a state transfer matrix that depends on electricity price, and establish a social welfare maximization model. Furthermore, the distributed RTP strategy is introduced to solve the model, which decomposes the model into supply-side and consumption-side. In addition, we propose an improved simulated annealing (SA) algorithm, using the mixing perturbation to limit large magnitudes. Extensive experiments demonstrate that the proposed framework is able to increase the convergence rate.