A three-dimensional (3-D) tomography technique is developed for the bolometry system in the Large Helical Device using the EMC3-EIRENE-defined mesh coordinates and the relative gradient smoothing extended to 3-D space. We utilize two types of bolometers, resistive bolometers and infra-red imaging video bolometers, to cover areas that are not visible with only one type of bolometer, the total channels of which are 1088. Although the resolution of the reconstructed solution rises to 59 400 voxels, we prove that the physically meaningful solution having little negative power is obtained by calculating geometry matrices with the tetrahedralization method and assessing the phantom emission and the synthetic data. Moreover, comparing solutions generated by conventional minimum Fisher regularization and 3-D extended relative gradient smoothing enables us to find that the latter provides a better solution.