  In this work, we propose that the odderon is a Regge odd-glueball tensor
spin-3. To demonstrate our proposal, we study the $pp$ and $p\bar p$ elastic
scattering by including contributions of the spin-3 odderon and spin-2 pomeron
exchange in the processes. The phenomenological effective Lagrangian approach
is used to calculate the $pp$ and $p\bar p$ elastic scattering amplitudes at
the tree level. In addition, a Donnachie-Landschoff ansatz of the odderon and
pomeron propagators has been used in this work. We fit the theoretical results
with the various experimental data of the $pp$ and $p\bar p$ scattering at the
TeV scale to determine the model parameters in the present work. By using the
model parameters, the Chew-Frautschi plot of the tensor odderon Regge
trajectory is evaluated. As a result, the odderon spin-3 mass is predicted to
be 3.2 GeV. In addition, the total cross-section of our model is compatible
with the results from TOTEM and its extrapolation from D0 collaboration.
Moreover, the total cross-section also satisfies the Friossart bound at the
Regge limit.
