Classical travel-time tomography struggles to resolve the heterogeneity within the medium. To address this challenge, this paper proposes a tomography method based on Hamiltonian Monte Carlo (HMC) sampling. In this method, forward modeling utilizes the fast marching method (FMM), governed by the Eikonal equation. For inversion, velocity parameters are expressed as probability distributions, and samples representing these parameters are obtained by employing a Markov chain. This chain is generated from the distributions. The Markov chain is controlled by an artificial Hamiltonian system. In this system, the models are treated as high-dimensional particles. These particles advance through trajectories in the extended phase space. HMC uses the derivatives of the forward equations to enable long-distance transitions between models. This approach enhances sample independence and maintains a high acceptance rate. Results demonstrate that this tomography method can accurately invert the position and shape of velocity anomalies, as well as the heterogeneity in stochastic medium models. This method provides a novel approach for seismic tomography. It can accurately characterize subsurface structures and is valuable for seismic exploration and geophysical studies.