We measured the fluorescence spectra of the whole blood, the red blood cell (RBC) and the hemoglobin using 457.9-nm Ar+ laser excitation. It was found that the fluorescence spectra of the whole blood and the RBC have much similarities in the intensity, the emission peaks and the emitting region, and abundant peaks can be found. But for the hemoglobin, fluorescence could only be found in the wavelength range 580-650 nm. It was concluded that in the wavelength range of 650-850 nm, the fluorescence spectra were emitted by the new fluorophores generated by the breakdown of some weak bonds on the RBC membrane, such as the C-C bond and the C-N bond. In the wavelength range of 590-650 nm, the fluorescence spectra are mainly emitted by the hemoglobin, but the hemoglobin solution of cracked RBC has a strong quencher effect on the fluorescence spectrum. The experimental result and the theoretical analysis are meaningful for the medical diagnostics and the therapy.