Aiming at the problems of the lack of reasonable judgment of fleet size and non-optimization of rebalancing for dockless bike-sharing station, based on the usage characteristics of dockless bike-sharing, this paper demonstrates that the Markov chain is suitable for the analysis of the fleet size of station. It is concluded that dockless bike-sharing Markov chain probability limit state (steady-state) only exists and is independent of the initial probability distribution. On that basis, this paper analyses the difficulty of the transition probability matrix parameter statistics and the power method of the bike-sharing Markov chain, and constructs the transition probability sparse matrix in order to reduce computational complexity. Since the sparse matrices may be reducible, the rank-one updating method is used to construct the transition probability random prime matrix to meet the requirements of steady-state size calculation. An iterative method for solving the steady-state probability is therefore given and the convergence speed of the method is analysed. In order to improve the practicability of the algorithm, the paper further analyses the construction methods of the initial values of the dockless bike-sharing and the transition probability matrices at different time periods in a day. Finally, the algorithm is verified with practical and simulation data. The results of the algorithm can be used as a baseline reference data to dynamically optimize the fleet size of dockless bike-sharing station operated by bike-sharing companies for strengthening standardized management.