Asymmetric transmission, defined as the difference between the forward and backward transmission, enables a plethora of applications for on-chip integration and telecommunications. However, the traditional method for asymmetric transmission is to control the propagation direction of the waves, hindering further applications. Metasurfaces, a kind of two-dimensional metamaterials, have shown an unprecedented ability to manipulate the propagation direction, phase, and polarization of electromagnetic waves. Here we propose and experimentally demonstrate a metasurface-based directional device consisting of a geometric metasurface with spatially rotated microrods and metallic gratings, which can simultaneously control the phase, polarization, and propagation direction of waves, resulting in asymmetric focusing in the terahertz region. These dual-layered metasurfaces for asymmetric focusing can work in a wide bandwidth ranging from 0.6 to 1.1 THz. The flexible and robust approach for designing broadband asymmetric focusing may open a new avenue for compact devices with potential applications in encryption, information processing, and communication.