Abstract: The axisymmetric cone, as a common configuration, is known to induce oblique detonation waves with a more complex structure compared to a wedge. Numerical simulations of the oblique detonation wave formed by a finite cone were conducted using the open-source code OpenFOAM, followed by discussions on the post-detonation flow field, detonation wave front structure, and detonation cell structure. The numerical results show that with the influence of the finite cone the post- detonation flow field is affected successively by Taylor-Maccoll flow and Prandtl-Meyer expansion waves. The pressure and Mach number along the streamlines at different positions on the detonation wave front exhibit oscillatory changes with the influence of these two physical processes and triple points on oblique detonation surfaces, and then tend to stabilize. Depending on the different post-detonation flow field, the detonation wave front structure is divided into four sections: smooth ZND-like structure, single-headed triple points cell-like structure, dual-headed triple points cell structure and dual-headed triple point structure influenced by Prandtl-Meyer. It is found that the upstream-facing triple points exhibits higher detonation intensity, i.e., higher Mach number and pressure, compared to the downstream-facing triple points in dual-headed triple points structure through shock polar analysis of wave systems near triple points. In conclusion, triple point traces are recorded to obtain four different cell structures: smooth planar structure, parallel line structure, oblique rhombus structure, and irregular oblique rhombus structure.