An optical absroption in the ferromagnetic insulator with the Dzyaloshinskii–Moriya interaction (DMI), theoretically and numerically is investigated. In other words, we investigate the optical absroption, σ(ω), of the spin Lieb nanolattice (SLN) a face-centered square lattice, subjected to a light spectrum with frequency ω. Using linear response theory and Green's function approach, the frequency dependence of optical conductivity (OC) has been obtained in the context of Heisenberg Hamiltonian. At low frequencies, the OC is found to be monotonically increasing with frequency for next-nearest neighbor (NNN) coupling, DMI strength (DMIS) and temperature. Also we have found that OC has a peak (absorption). Eventually, we are investigated the effect of magnetic field on the OC of this system.