Recently, a novel two-dimensional (2D) Dirac material BeN 4 monolayer has been fabricated experimentally through high-pressure synthesis. In this work, we investigate the thermal properties of a new class of 2D materials with a chemical formula of MN 4 (M = Be and Mg) using first-principles calculations. First, the cohesive energy and phonon dispersion curve confirm the dynamical stability of BeN 4 and MgN 4 monolayers. Besides, BeN 4 and MgN 4 monolayers have the anisotropic lattice thermal conductivities of 842.75 (615.97) W m -1 K -1 and 52.66 (21.76) W m -1 K -1 along the armchair (zigzag) direction, respectively. The main contribution of the lattice thermal conductivities of BeN 4 and MgN 4 monolayers are from the low frequency phonon branches. Moreover, the average phonon heat capacity, phonon group velocity, and phonon lifetime of BeN 4 monolayer are 3.54 × 10 5 J K -1 m -3 , 3.61 km s -1 , and 13.64 ps, which are larger than those of MgN 4 monolayer (3.42 × 10 5 J K -1 m -3 , 3.27 km s -1 , and 1.70 ps), indicating the larger lattice thermal conductivities of BeN 4 monolayer. Furthermore, the mode weighted accumulative Grüneisen parameters (MWGPs) of BeN 4 and MgN 4 monolayers are 2.84 and 5.62, which proves that MgN 4 monolayer has stronger phonon scattering. This investigation will enhance an understanding of thermal properties of MN 4 monolayers and drive the applications of MN 4 monolayers in nanoelectronic devices.