A numerical model for the self-burial of a pipeline trench is developed. Morphological evolutions of a pipeline trench under steady-current or oscillatory-flow conditions are simulated with/without a pipeline inside the trench. The oscillatory flow in this study represents the action of waves. The two-dimensional Reynolds-averaged continuity and Navier-Stokes equations with the standard k-ε turbulence closure, as well as the sediment transport equations, are solved with the finite difference method in a curvilinear coordinate system. Both bed and suspended loads of sediment transport are included in the morphological model. Because of the lack of experimental data on the backfilling of pipeline trenches, the numerical model is firetly verified against three closely-relevant experiments available in literature. A detailed measurement of the channel migration phenomenon under steady currents is employed for the assessment of the integral performance of the model. The two experimental results from U-tube tests are used to validate the model's ability in predicting oscillatory flows. Different time-marching schemes are employed for the morphological computation under unidirectional and oscillatory conditions. It is found that vortex motions within the trench play an important role in the trench development.