A structurally stable stacked multilayer carbonitride is predicted with the aid of ab initio calculations. This carbonitride consists of C3N tetrahedra, and is similar to T-carbon and thus named T-C3N. Its 2-dimensional (2D) monolayer is also carefully investigated in this work. The studies on electronic properties reveal that bulk and 2D T-C3N are insulators with a 5.542 eV indirect band gap and a 5.741 eV direct band gap, respectively. However, the monolayer T-C3N exhibits an excellent uniform porosity. Its 5.50 Å pore size is perfect for water nanofiltration. The adsorption and permeation of water molecules on the monolayer T-C3N are investigated. Its promising potential application in highly efficient nanofiltration membranes for seawater desalination is discussed.