Photosystem I (PSI) functions to harvest light energy for conversion into chemical energy. The organisation of PSI is variable depending on the species of organism. Here we report the structure of a tetrameric PSI core isolated from a cyanobacterium, Anabaena sp. PCC 7120, analysed by single-particle cryo-electron microscopy (cryo-EM) at 3.3 Å resolution. The PSI tetramer has a C2 symmetry and is organised in a dimer of dimers form. The structure reveals interactions at the dimer-dimer interface and the existence of characteristic pigment orientations and inter-pigment distances within the dimer units that are important for unique excitation energy transfer. In particular, characteristic residues of PsaL are identified to be responsible for the formation of the tetramer. Time-resolved fluorescence analyses showed that the PSI tetramer has an enhanced excitation-energy quenching. These structural and spectroscopic findings provide insights into the physiological significance of the PSI tetramer and evolutionary changes of the PSI organisations.