  In this paper, masses and radii of $\Sigma^-_u$ states hybrid charmonium
mesons are calculated by numerically solving the Schr\"odinger equation with
non-relativistic potential model. Results for calculated masses of $\Sigma^-_u$
states charmonium hybrid mesons are found to be close to the results obtained
through lattice simulations. Calculated masses are used to construct Regge
trajectories. It is found that the trajectories are almost linear and parallel.
