We explore the nonreciprocity of spin-wave excitations in the Rashba-Hubbard ferromagnet on a square lattice. Our study reveals that the propagation of spin-wave excitations exhibit non-reciprocal behavior, i.e., spin waves traveling in opposite directions display asymmetry in energy dispersion ω(q)=ω(−q), which also results in an asymmetric behavior of group velocity, spin stiffness, etc. We find that this asymmetric behavior arises only when the magnetic moments are aligned inside the atomic plane, while the excitations remain symmetric for out-of-plane magnetization. The first dominating term in the low-energy dispersion is linear. However, if the magnetic moments are out-of-plane, then the first dominant term is quadratic instead. The low-energy non-quadratic behavior is examined in the intermediate-to-strong coupling regime for various strengths of Rashba spin-orbit coupling.