Quantum tomography is one of the major challenges of large-scale quantum information research due to the exponential time complexity. In this Letter, we develop and apply a Bayesian state estimation method to experimentally demonstrate quantum overlapping tomography [Phys. Rev. Lett. 124, 100401 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.100401], a scheme intent on characterizing critical information of a many-body quantum system in logarithmic time complexity. By comparing the measurement results of full-state tomography and overlapping tomography, we show that overlapping tomography gives accurate information of the system with much fewer state measurements than full-state tomography.