Topological defects in magnetism have attracted great attention due to fundamental research interests and potential novel spintronics applications. Rich examples of topological defects can be found in nanoscale non-uniform spin textures, such as monopoles, domain walls, vortices, and skyrmions. Recently, skyrmions stabilized by the Dzyaloshinskii-Moriya interaction have been studied extensively. However, the stabilization of antiskyrmions is less straightforward. Here, using numerical simulations we demonstrate that antiskyrmions can be a stable spin configuration in the presence of anisotropic Dzyaloshinskii-Moriya interaction. We find current-driven antiskyrmion motion that has a transverse component, namely antiskyrmion Hall effect. The antiskyrmion gyroconstant is opposite to that for skyrmion, which allows the current-driven propagation of coupled skyrmion-antiskyrmion pairs without apparent skyrmion Hall effect. The antiskyrmion Hall angle strongly depends on the current direction, and a zero antiskyrmion Hall angle can be achieved at a critic current direction. These results open up possibilities to tailor the spin topology in nanoscale magnetism, which may be useful in the emerging field of skyrmionics.