Based on density functional theory (DFT), a new silicon allotrope (C2-Si) is proposed in this work. The mechanical stability and dynamic stability of C2-Si are examined based on the elastic constants and phonon spectrum. According to the BH/GH values, C2-Si has ductility under ambient pressure; compared with Si64, Si96, I4/mmm and h-Si6, C2-Si is less brittle. Within the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional, C2-Si is an indirect narrow band gap semiconductor, and the band gap of C2-Si is only 0.716 eV, which is approximately two-thirds that of c-Si. The ratios of the maximum and minimum values of the Young's modulus, shear modulus and Poisson's ratio in their 3D spatial distributions for C2-Si are determined to characterize the anisotropy. In addition, the anisotropy in different crystal planes is also investigated via 2D representations of the Young’s modulus, shear modulus and Poisson’s ratio. In addition, among more than ten silicon allotropes, C2-Si has the strongest absorption ability for visible light.