Multiple far-red light-adapted photosystem I (FR-PSI) reaction centers are recently found to work in oxygenic photosynthesis. They contain a small amount of a new type pigment chlorophyll f (Chl f) in addition to the major pigment chlorophyll a (Chl a). FR-PSI differs from the conventional PSIs in plants and cyanobacteria, which use only visible light absorbed by Chl a, although the mechanism of FR-PSI is not fully clear yet. We theoretically studied the light-harvesting mechanism of FR-PSI of Fischerella thermalis PCC 7521, in which a small amount of Chl f transfers the excitation energy of FR-light uphill to Chl a. We constructed two types of exciton models for FR-PSI using pigment arrangements based on the structural information. A model that assumes the same site energy value for all of the antenna Chl a molecules reproduced most of the experimentally obtained properties. The transient absorption spectra, excitation energy relaxation, and mean first passage time (MFPT) of the excitation energy transfer from Chls f and a to the special pair P700 (a pair of Chl a/Chl a') were numerically calculated. The model, however, could not reproduce the low but distinct absorption intensity between the Chl a- and Chl f-bands and predicted a rather slow energy transfer from Chl f to P700. Advanced "modified models" further tested the effect of modification of the site energy values at individual antenna Chl a molecules. The optical properties and MFPTs of FR-PSI were calculated for each model with modified site energy values to evaluate the uphill light-harvesting process. The analysis showed that Chl a-1131 and -1222 play key roles in the light-harvesting process from Chl f molecules to P700, regardless of the excitation wavelength. The locations and site energy values of these Chl a molecules were found to be essential to reproduce the unique uphill energy transfer function of FR-PSI.