LSSmKate1 and LSSmKate2 are monomeric red fluorescent proteins (RFPs) with large Stokes shifts (LSS). The hydrogen-bonding (H-bonding) network within LSSmKatel or LSSmKate2, which is composed of a chromophore and some surrounding amino acid residues, supports their special spectral properties. In this work, we propose H-bonding complex models to simulate the H-bonding network of LSSmKatel and LSSmKate2 and employ the time-dependent density functional theory combining with the sum-overstates method to calculate their one- and two-photon absorption characters. We discuss the influence of the hydrogen bond on the one- and two-photon absorption properties of these H-bonding complexes through intermolecular hyperconjugation of the hydrogen-bond form.