Because the single-layer CrI₃ is a half semiconductor with indirect band gap and magnetic anisotropy, it has received much attention in the spintronic, magneto-electronic and magnetic storage applications. However, the knowledge of the dependence of carrier mobility and optical property on strain is still rather limited. The uniaxial and biaxial strain dependence of electronic, transport, optical and magnetic properties of single-layer CrI₃ are systematically investigated by using first-principles calculations, and the results are compared with experimental results. The electronic structures under different strains are first calculated by using the accurate HSE06 functional, then the carrier mobility is estimated by the deformation potential theory and the dielectric function is obtained to estimate the optical absorption especially in the visible light range. Finally, the magnetic anisotropy energy used to estimate the magneto-electronic properties is studied by the Perdew-Bueke-Ernzerhof functional including the spin-orbit coupling. It is found that the ferromagnetic CrI₃ is an indirect and half semiconductor with band gap 2.024 eV, \Delta \textCBM = 1.592 eV, \Delta \textVBM = 0.238 eV and can be driven into AF-Néel antiferromagnetic phase by applying –6% to –8% (compressive) biaxial stain, exhibiting excellent agreement with the results from the literature. It is found that of single-layer CrI₃ has very low carrier mobility with a value within 10 cm²·V^–1·s^–1 due to the large effective mass and small in-plane stiffness can be remarkably increased by increasing biaxial compression strain attributed to the reduced effective mass. A high electron mobility 174 cm²·V^–1·s^–1 is obtained in the zigzag direction by applying a –8% biaxial strain reaching the level of monolayer MoS₂. The calculated imaginary component of dielectric function along the x (y) direction having two peaks (I, II) in the visible light range is obviously different from that along the z direction, indicating that the single-layer CrI₃ has optical anisotropy, demonstrating the good agreement with results from the literature. It is found that the imaginary part of dielectric function shows that an obvious redshift and peak (I, II) values strongly increase with the increase of compressive strain (biaxial), showing good agreement with the calculated electronic structures and indicating that monolayer CrI₃ possesses high optical adsorption of visible light under a compressive biaxial strain. Furthermore, it is found that the magnetic anisotropy energy of monolayer CrI₃ mainly stemming from the orbital magnetic moment of Cr ions remarkably increases from 0.7365 to 1.08 meV/Cr with g compressive strain increasing. These results indicate that the optoelectronic property of single-layer CrI₃ can be greatly improved by applying biaxial compressive strain and the single-layer CrI₃ is a promising material for applications in microelectronic, optoelectronic and magnetic storage.