We measured picosecond time-resolved fluorescence of intact Photosystem I complexes from Chlamydomonas reinhardtii and Arabidopsis thaliana. The antenna system of C. reinhardtii contains about 30-60 chlorophylls more than that of A. thaliana, but lacks the so-called red chlorophylls, chlorophylls that absorb at longer wavelength than the primary electron donor. In C. reinhardtii, the main lifetimes of excitation trapping are about 27 and 68 ps. The overall lifetime of C. reinhardtii is considerably shorter than in A. thaliana. We conclude that the amount and energies of the red chlorophylls have a larger effect on excitation trapping time in Photosystem I than the antenna size.