Three-dimensional (3D) topological Dirac semimetal is a new kind of material that has a linear energy dispersion in 3D momentum space and can be viewed as an analog of graphene. Extensive efforts have been devoted to the understanding of bulk materials, but yet it remains a challenge to explore the intriguing physics in low-dimensional Dirac semimetals. Here, we report on the synthesis of Cd3As2 nanowires and nanobelts and a systematic investigation of their magnetotransport properties. Temperature-dependent ambipolar behavior is evidently demonstrated, suggesting the presence of finite-size of bandgap in nanowires. Cd3As2 nanobelts, however, exhibit metallic characteristics with a high carrier mobility exceeding 32,000 cm2V-1s-1 and pronounced anomalous double-period Shubnikov-de Haas (SdH) oscillations. Unlike the bulk counterpart, the Cd3As2 nanobelts reveal the possibility of unusual change of the Fermi sphere owing to the suppression of the dimensionality. More importantly, their SdH oscillations can be effectively tuned by the gate voltage. The successful synthesis of Cd3As2 nanostructures and their rich physics open up exciting nanoelectronic applications of 3D Dirac semimetals.