The discharge channel is a crucial diagnostic tool for the properties of gas switch. However, the single-view images is hardly to understand the inherently the discharge channel characteristics of trigger electrode. A reconstruction method of the discharge channel in gas switch is proposed based on multi-axis tomography technique, which uses very few projections of optical image to reconstruct the location of multichannel discharge in annular electrodes. In this paper, we present an algorithm, TVM-OSEM (total variation minimization ordered subsets expectation maximization) effectively removes artifacts on the reconstructed images to improve the accuracy of the diagnosis of discharge channels. The method is validated against simulations of radiator with high-density-difference boundary. The calculated discharge channel distribution from one experiment is presented.