Discovering highly in-plane anisotropic two-dimensional (2D) semiconductors with multiple superior properties (good stability, widely tunable bandgap and high mobility) are of great interest for fundamental studies and for developments of novel (opto)electronic devices. By means of state-of-the-art first-principles calculations, herein we present a thorough investigation on the stability, electronic properties and promising applications of previously unexplored 2D semiconductors - gold-selenium (β-AuSe) with strong in-plane anisotropy, whose layered bulk counterpart was synthesized fifty years ago. We show that they have stable structures, widely tunable bandgap varying from 1.66 eV in monolayer to 0.70 eV in five-layer, strong light absorption coefficient (∼10 cm) within the whole visible light range, and high/ultrahigh carrier mobility (10-10 cm V s). More importantly, they show highly in-pane anisotropic behaviors in absorption coefficients, photoconductance and carrier mobility. Especially, the anisotropic ratio of carrier mobility is much higher than the literature reported ones. The above findings show that the in-plane anisotropic 2D β-AuSe are promising candidates for developing polarization-sensitive photodetectors, synaptic devices and micro digital inverters based on multiple superior properties and highly anisotropic behaviors. Besides, few-layer β-AuSe systems can serve as channel materials in field-effect transistors with high mobility or be applied in solar cells with strong light absorption. Our findings demonstrate that few-layer 2D β-AuSe have great potential for multifunctional applications and thus stimulate immediately experimental interests.