We predicted, using first principles calculation, that AMgBi (A=K, Rb, Cs) are symmetry-protected topological semimetals near the boundary of type-I and type-II Dirac semimetal phases, dubbed topological critical Dirac semimetals. Doping Rb or Cs into KMgBi can drive the transition between the two phases. An effective theory is developed to describe the bands near the Fermi energy, by which we calculate the surface Fermi arcs and the Landau levels throughout the transition. We predict the key features of critical Dirac semimetals that can be observed in photoemission, quantum oscillation and transport measurements. Topological semimetals (TSs) are semimetals whose Fermi surfaces carry nontrivial topological numbers. These quantum numbers lead to a series of exotic effects such as the existence of Fermi arcs on the surface 1,2 and the chiral anomaly 3,4 in the bulk transport. Crystal symmetries afford us a large variety of topological semimetals including Weyl semimetals (WS) 1,5-12 , Dirac semimetals (DS) [13][14][15] and nodal line semimetals 16,17 . For Weyl/Dirac semimetals, a further distinction has been made between the type-I and the type-II classes 18 , where the Fermi surfaces (at ideal half-filling) are point-like and pocket-like, respectively. The physical consequences of both types have been studied 19,20 . For its unique feature and potential application, TSs have drawn great attention in the field of topological materials. In recent years, great progress has been made both theoretically and experimentally. Na 3 Bi and Cd 3 As 2 have been predicted to be three-dimensional (3D) linear DSs theoretically 14,15 and have been verified by angle-resolved photoemission spectroscopy (ARPES) measurements 21,22 . In transport experiments, Cd 3 As 2 and several other DSs exhibit strong linear magnetoresistance 23,24 , which is also a strong evidence for DSs.In this Letter, we propose, by using first principles calculation, a family of materials, AMgBi, as topological semimetals that lie in between the type-I and the type-II Dirac semimetals, where A is an alkaline metal (A=K, Rb, Cs). While KMgBi, which has been synthesized 25 , is a type-I Dirac semimetal, both RbMgBi and CsMgBi, are both type-II Dirac semimetals. Doping Rb and Cs into KMgBi hence drives a transition from type-I to type-II Dirac semimetals. Hence we call these compounds topological critical Dirac semimetals, which can help us understand this topological phase transition.To further study the physical observables in these compounds, we develop an effective model that captures the key features near the Fermi energy throughout the topological transition. Using the model, we computed the surface states with Fermi arcs and also the Landau levels in the presence of magnetic field. These results can be directly observed in ARPES, Scanning Tunneling Microscope (STM) and transport measurements.Method and Crystal Structure Our calculations are performed using density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP)...