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Three-dimensional topological Dirac semimetals represent a novel state of quantum matter with exotic electronic properties, in which a pair of Dirac points with a linear dispersion along all momentum directions exists in the bulk. Herein, by using first-principles calculations, we discover the metastable allotropes of Ge and Sn in the staggered layered dumbbell structure, named germancite and stancite, to be Dirac semimetals with a pair of Dirac points on their rotation axis. On the surface parallel to the rotation axis, a pair of topologically nontrivial Fermi arcs are observed and a Lifshitz transition is found by tuning the Fermi level. Furthermore, the quantum thin film of germancite is found to be an intrinsic quantum spin Hall insulator. These discoveries suggest novel physical properties and future applications of the metastable allotrope of Ge and Sn., W.C. and W.D. acknowledge support from the Ministry of Science and Technology of China and theNational Natural Science Foundation of China (Grant No. 11334006). A.R. acknowledges financial support from the European Research Council Grant DYNamo (ERC-2010-AdG No. 267374) Spanish Grants (FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), and EC project CRONOS (280879-2 CRONOS CPFP7). P.T. and S.-C.Z. acknowledge NSF under Grant No. DMR-1305677 and FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.