We report the quantum transport properties of Cd₃As₂ single crystals in a magnetic field. A large linear quantum magnetoresistance is observed near room temperature. With decreasing temperature, the Shubnikov-de Haas oscillations appear in both the longitudinal resistance R(xx) and the transverse Hall resistance R(xy). From the strong oscillatory component ΔR(xx), a linear dependence of the Landau index n on 1/B is obtained, and it gives an n-axis intercept between 1/2 and 5/8. This clearly reveals a nontrivial π Berry's phase, which is a distinguished feature of Dirac fermions. Our quantum transport results provide bulk evidence for the existence of a three-dimensional Dirac semimetal phase in Cd₃As₂.