LaWN3, a novel nitride perovskite, have been synthesized and its piezoelectric properties have been investigated (TALLEY K. R. et at., Science, 374 (2021) 1488). However, the understanding of its ferroelectric properties under the external strain is still lacking. Here, the misfit-strain-dependent coupling between anti-ferrodistortions (AFD) and ferroelectric (FE) distortions has been studied by using a first-principle approach. It can be observed that AFD and FE distortions can work cooperatively with each other as the compressive strain increases, and the coupling energy between them is found to work in different ways under various strains. Our results show that the coupling tends to stabilize the ground structure when the compressive strain is smaller than -1.9%, it works oppositely when the compressive strain becomes larger than 1.9%. Our results can provide us with more hints about the influence of the epitaxial strains on the intrinsic coupling behavior in the perovskite ferroelectric compounds, which is very important for us to design and fabricate new kinds of functional materials.