The intriguing properties of phosphorene motivate scientists to further explore the structures and properties of phosphorus materials. Here, we report a new allotrope named K4 phosphorus composed of three-coordinated phosphorus atoms in non-layered structure which is not only dynamically and mechanically stable, but also possesses thermal stability comparable to that of the orthorhombic black phosphorus (A17). Due to its unique configuration, K4 phosphorus exhibits exceptional properties: it possesses a band gap of 1.54 eV which is much larger than that of black phosphorus (0.30 eV), and it is stiffer than black phosphorus. The band gap of the newly predicted phase can be effectively tuned by appling hydrostastic pressure. In addition, K4 phosphorus exibits a good light absorption in visible and near ultraviolet region. These findings add additional features to the phosphorus family with new potential applications in nanoelectronics and nanomechanics.