On-chip polarization-sensitive photodetectors are highly desired for ultra-compact optoelectronic systems. It has been demonstrated that polarization-sensitive photodetection can be realized using intrinsic chiral and anisotropy materials. However, these photodetectors can only realize the detection of either circularly polarized light (CPL) or linear polarized light (LPL) and are not applicable to multiple-polarization-sensitive photodetection. Herein, we experimentally demonstrate a metasurface-integrated semiconductor to realize multiple-polarization-sensitive photodetection at visible wavelengths. This device is composed of a MoSe2 monolayer on an H-shaped plasmonic nanostructure. The geometric chirality and anisotropy of the H-shaped nanostructure result in CPL and LPL resolved optical responses. By integrating a plasmonic metasurface with monolayer MoSe2, we converted polarization-sensitive optical absorption to the polarization-sensitive photocurrent of the device through the photoconductive effect. Polarization-sensitive photocurrent responses to both CPL and LPL are systematically investigated, which demonstrate a high photocurrent circular dichroism (CD) of 0.35 at a wavelength of 810 nm and photocurrent linear polarization (LP) of 0.4 at a wavelength of 633 nm. Our results provide a potential pathway to realize multiple-polarization-sensitive applications in medicine analysis, biology, and remote sensing.