By means of comprehensive density functional theory (DFT) computations, we designed a new two-dimensional (2D) structure of silicon, namely, tetra-silicene. In tetra-silicene, each silicon atom binds with four neighboring Si atoms to form a 2D network composed of only tetragons. Our DFT computations demonstrate that tetra-silicene is of rather high experimental feasibility, as indicated by its considerable cohesive energy, all positive modes in the phonon spectrum, and the well maintained structure after 10 ps first-principles molecular dynamics simulations at 500 K. Tetra-silicene has rather intriguing mechanical properties featured with unusual negative Poissons ratios. Remarkably, different from hexagonal silicene (hexa-silicene) which is semi-metallic without a band gap, tetra-silicene is semiconducting with an appreciable indirect band gap of 0.19 eV, and it has a considerable carrier mobility of 1639.07 cm(2) V-1 s(-1). Encouragingly, our simulations suggest that tetra-silicene can be flexibly produced from hexa-silicene via mechanical conversion. Once synthesized, tetra-silicene would find many important applications in electronics and mechanical devices.