Topological superconductivity has attracted intensive interest for its ability of hosting Majorana zero mode and implementing in topological quantum computations. Based on the first-principles calculations and the analysis of the effective BdG Hamiltonian, we demonstrate that 1T -TiTe 2 is a topological metal hosting Dirac cone type of surface states near the Fermi level, and it exhibits a normal-topological-normal superconducting phase transition as a function of the chemical potential. These results point out a new promising topological superconductor without random dopant, in which the influence of the impurity may be greatly reduced. Furthermore, our calculations also suggest that the transition metal intercalated Ti(Se 1−y Te y ) 2 is also a highly possible route to realize topological superconductivity and Majorana zero modes.