A new analytical method based on the surface plasmon resonance (SPR) technique is presented, with which SPR curves for both wavelength and angular modulations can be obtained simultaneously via only a single scan of the incident angle. Using this method, the SPR responses of TiO2-coated Cu films are characterized in the wavelength range from 600 nm to 900 nm. For the first time, we determine the effective optical constants and the thicknesses of TiO2-coated Cu films using the SPR curves of wavelength modulation. The sensitivities of prism-based SPR refractive index sensors using TiO2-coated Cu films are investigated theoretically for both wavelength and angular modulations, the results show that in the case of sensitivity with wavelength modulation, TiO2-coated Cu films are not as good as the Au film, however, they are more suitable than the Au film for SPR refractive index sensors with angular modulation because a higher sensitivity can be achieved.