The twistronics of the atomic-thick two-dimensional (2D) van der Waals materials has opened a new venue to investigate the interlayer coupling. Till now, most studies focus on the twist of atomic lattices and the resulted moiré superstructures, while the reports about the twist of charge density waves (CDWs), the superstructures of which are from individual layers are limited. Here, using molecular beam epitaxy, we construct bilayer (BL) 1T-NbSe2 vertical structures. With high resolution scanning tunneling microscopy observations, we identify two cases of CDW twisted stacking with atomic precision. The typical twist angles are 0° and 60° between the 1st and the 2nd layer, although the top Se atomic lattices of these two layers are parallel. Compared to the single layer case, the dI/dV at BL shows an insulator-to-metal transition, with the Hubbard bands shrinking towards the Fermi level (E F). More intriguingly, interlayer coupling states rise near E F, which are related to the CDW twist angles. These findings give fresh insight into the engineering of 2D materials by CDW twisting and are potentially applicable for future nanoelectronic devices.