The development of information technology puts forward huge demand for electronic materials with high dielectric constants; first-principles calculations and simulations have been demonstrated as an efficient technique for screening and exploring novel dielectric materials. In the present study, first-principles calculations combined with density functional perturbation theory are employed to study the dielectric properties of two newly discovered layered nitrides SrHfN2 and SrZrN2 under strain. By analyzing the evolution of lattice distortion, dielectric constant, Born effective charge, and phonon modes along with the applied strain, we find that the biaxial strain and isotropic strain can effectively modulate the dielectric constant. The two nitrides SrHfN2 and SrZrN2 are dynamically stable up to biaxial tensile strains of 2.1% and 1.8%, and the dielectric constants have been enlarged to about 500 and 2000. Furthermore, the dielectric constant is dramatically enhanced by 15 (9) times to a maximum value of ∼2600 (2700) under an isotropic tensile strain of 1.2% (0.7%) for SrHfN2 (SrZrN2), which is mainly due to the softening of the lowest-frequency infrared-active phonon mode and the increasing octahedral distortion degree. Particularly, the ionic contribution of the dielectric constant shows very remarkable anisotropy and plays a dominant role in the change of the dielectric constant, whose in-plane components exhibit giant enhancement by 18 (10) times for SrHfN2 (SrZrN2). This work not only sheds light on the experimentally observed high dielectric constants of SrHfN2 and SrZrN2, but also provides an effective route to regulate the anisotropic dielectric constants by applied strain, which indicates promising applications in optical and electronic devices.