An optical trap has been combined with a Raman spectrometer to make high-resolution measurements of Raman spectra of optically-immobilized, single, live red (RBC) and white blood cells (WBC) under physiological conditions. Tightly-focused, near infrared wavelength light (1064 nm) is utilized for trapping of single cells and 785 nm light is used for Raman excitation at low levels of incident power (few mW). Raman spectra of RBC recorded using this high-sensitivity, dual-wavelength apparatus has enabled identification of several additional lines; the hitherto-unreported lines originate purely from hemoglobin molecules. Raman spectra of single granulocytes and lymphocytes are interpreted on the basis of standard protein and nucleic acid vibrational spectroscopy data. The richness of the measured spectrum illustrates that Raman studies of live cells in suspension are more informative than conventional micro-Raman studies where the cells are chemically bound to a glass cover slip.