Via first-principles calculations, we investigate heterovalent doping of all-inorganic perovskite CsPbI3 with In, Sb, Tl and Bi, focusing on the electronic, optical and energetic properties. Results show that p-type doping can be achieved by replacing Pb with In and Tl, while Sb and Bi make CsPbI3 n-type doped. Energy gap of CsPbI3 can be tuned from 1.2 to 0.4 eV, leading to enhanced optical absorption at visible light region. Furthermore, we show that In, Sb and Bi are much easier to be doped, which explains available experiments. These findings may shed light on fabrication of optoelectronic devices based on perovskites.