Janus nanotubes originating from rolling up asymmetric dichalcogenide monolayers have shown unique properties compared to their 2D and 3D counterparts. Most of the work on Janus nanotubes is focused on single-wall (SW) tubes. In this work, we have investigated the structural and electronic properties of double wall (DW) MoSTe nanotubes using Density Functional Theory (DFT). The most stable DW, corresponding to a minimum of the strain energy, is formed by combining 16- and 24-unit cells for the inner and outer tubes. This DW configuration shows a slightly smaller inner diameter than the SW tube, which was formed by 18-unit cells due to the intra-wall interaction. The investigation of the band gaps of 2D structures under strain and SW/DW nanotubes revealed that the curvature of the nanotube and the strain induced when forming the tube are the two primary factors enabling the band gap tuning. Moreover, we found that the band gaps of the DW MoSTe tubes close, compared to the SWs, generating tubes with a metallic-like behavior. This property makes DW MoSTe nanotubes promising for electrochemical applications.