Density functional theory-based simulations are applied to study the electronic structures, carrier masses, carrier mobility and carrier relaxation times in bulk and two-dimensional (2D) Zn2(V,Nb,Ta)N3 ternary nitrides. Bulk Zn2(V,Nb,Ta)N3 possess moderate band gap sizes of 2.17 eV, 3.11 eV, and 3.40 eV, respectively. Two-dimensional Zn2(V,Nb,Ta)N3 have slightly higher band gap sizes of 2.77 eV, 3.33 eV, and 3.23 eV, respectively. Carrier mass, carrier mobility and carrier relaxation time are found to be anisotropic in all the studied structures. Bulk and 2D samples show an order of magnitude higher electron mobility compared to hole mobility. The highest electron mobility in bulk Zn2NbN3 and Zn2TaN3 is about ∼103 cm2 V-1 s-1. Importantly, for 2D Zn2NbN3, an abnormally high electron mobility of 1.67 × 104 cm2 V-1 s-1 is observed, which is not inferior to the highest known electron mobility values in 2D materials. Such a high electron mobility in 2D Zn2NbN3 can be attributed to a strong delocalization of the conduction band minimum, which is responsible for electron transport. Therefore, this work opens up new materials for high performance nanodevices, such as tandem solar cells and field-effect transistors. This study also provides deep physical insights into the nature of carrier transport mechanisms in bulk and 2D Zn2(V,Nb,Ta)N3 ternary nitrides.