In this paper, we give some characterizations of Frenet curves in 3-dimensional $\delta$-Lorentzian trans-Sasakian manifolds. We compute the Frenet equations and Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional $\delta$-Lorentzian trans-Sasakian manifolds. Finally, we give some results for these curves.