A theoretical model of the far-red-light-adapted photosystem I (PSI) reaction center (RC) complex of a cyanobacterium, Acaryochloris marina (AmPSI), was constructed based on the exciton theory and the recently identified molecular structure of AmPSI by Hamaguchi et al. (Nat. Commun., 2021, 12, 2333). A. marina performs photosynthesis under the visible to far-red light (400–750 nm), which is absorbed by chlorophyll d (Chl-d). It is in contrast to the situation of all the other oxygenic photosynthetic processes of cyanobacteria and plants, which contains chlorophyll a (Chl-a) that absorbs only 400–700 nm visible light. AmPSI contains 70 Chl-d, 1 Chl-d′, 2 pheophytin a (Pheo-a), and 12 carotenoids in the currently available structure. A special pair of Chl-d/Chl-d′ acts as the electron donor (P740) and two Pheo-a act as the primary electron acceptor A0 as the counterparts of P700 and Chl-a, respectively, of Chl-a-type PSIs. The exciton Hamiltonian of AmPSI was constructed considering the excitonic coupling strength and site energy shift of individual pigments using the Poisson-TrESP (P-TrESP) and charge density coupling (CDC) methods. The model was constructed to fit the experimentally measured spectra of absorption and circular dichroism (CD) spectra during downhill/uphill excitation energy transfer processes. The constructed theoretical model of AmPSI was further compared with the Chl-a-type PSI of Thermosynechococcus elongatus (TePSI), which contains only Chl-a and Chl-a′. The functional properties of AmPSI and TePSI were further examined by the in silico exchange of Chl-d by Chl-a in the models.