  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 1$T$-TiTe$_2$ is a
topological metal hosting Dirac cone type of surface states near the Fermi
level, and it exhibits a normal-topological-normal superconductivity 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 TSC and MZMs.
