Field-driven magnetic domain wall propagation in ferromagnetic nanostrips with trapezoidal cross section has been systematically investigated by means of micromagnetic simulation. Asymmetric dynamic behaviors of domain wall, depending on the propagation direction, were observed under an external magnetic field. When the domain walls propagate in the opposite direction along the long axis of the nanostrip, the Walker breakdown fields as well as the average velocities are different. The asymmetric landscape of demagnetization energies, which arises from the trapezoidal geometry, is the main origin of the asymmetric propagation behavior. Furthermore, a trapezoid-cross-section nanostrip will become a nanotube if it is rolled artificially along its long axis, and thus a two-dimensional transverse domain wall will become a three-dimensional one. Interestingly, it is found that the asymmetric behaviors observed in two-dimensional nanostrips with trapezoidal cross section are similar with some dynamic properties occurring in three-dimensional nanotubes.