Recently, C568 has emerged as a new carbon allotrope, which shows semiconducting properties with a band gap around 1 eV and has attracted much attention. In this work, the external strain effects on the electronic properties of C568 have been studied theoretically through first-principle calculations. The numerical results show that while in-plane uniaxial and biaxial strains both reduces the band gap of C568 in case of tensile strain, their effects are quite different in the case of compressive strain. With increasing compressive uniaxial strain, the band gap of C568 first increases, and then dramatically decreases. In contrast, the application of compressive biaxial strain up to –10% only leads to a slight increase of band gap. Moreover, an indirect-to-direct gap transition can be realized under both types of compressive strain. The results also show that the optical anisotropy of C568 can be induced under uniaxial strain, while biaxial strain does not cause such an effect. These results indicate good strain tunability of the band structure of C568, which could be helpful for the design and optimization of C568-based nanodevices.