Searching for Majorana bound states has become an important topic because of its potential applications in topological quantum computing. 2M-phase WS2, a newly synthesized superconductor, not only presents the highest superconducting transition temperature (Tc = 8.8 K) among the intrinsic transition metal dichalcogenides but also is predicted to be a promising candidate as a topological superconductor. Using scanning tunnelling microscopy, we observe a U-shaped superconducting gap in 2M-WS2. Probable Majorana bound states are observed in magnetic vortices, which manifest as a non-split zero-energy state coexisting with the ordinary Caroli–de Gennes–Matricon bound states. Such non-split bound states in 2M-WS2 show highly spatial anisotropy, originating from the anisotropy of the superconducting order parameter and Fermi velocity. Due to its simple layered structure and substitution-free lattice, 2M-WS2 can be a building block to construct novel heterostructures and provides an ideal platform for the study of Majorana bound states.