Abstract Exploring two-dimensional (2D) tetragonal carbon nitride materials is significant for unlocking new physical properties beyond those offered by traditional hexagonal lattices. In this work, we propose three theoretically stable 2D carbon nitride monolayers with tetragonal lattices, namely T-C3N, P-C3N, and PH-C5N4. Electronic structure calculations indicate that all three monolayers exhibit semiconducting characteristics, with T-C3N showing interesting flat band features. Additionally, these three carbon nitrides exhibit anisotropic and high carrier mobilities and excellent light absorption capabilities in the visible-light and near-infrared regions. Meanwhile, the calculated thermal conductivity (κp) of PH-C5N4 is 63.9 Wm−1K−1 at room temperature, significantly outperforming T-C3N (12.2 Wm−1K−1) and P-C3N (18.9 Wm−1K−1). Phonon scattering rates and Grüneisen parameters confirm the origin for the relatively high κp in PH-C5N4. Our study proposes three tetragonal carbon nitride structures with novel physical properties, which lays a theoretical foundation for the multifunctional applications of 2D carbon nitride materials.