Raman spectroscopy is a label-free and non-invasive method that measures the inelastic scattered light from a sample giving insight into the vibration eigenmodes of the excited molecules. Raman spectroscopy provides a detailed chemical composition of the sample, constituting a sort of its chemical fingerprint. Although Raman spectroscopy is a useful technique to identify and quantify species in a given matrix, it has been severely limited in its applicability by fluorescence. Spectrally, this fluorescence occurs at the same wavelength as the Raman signal and is often several orders of magnitude more intense that the weak chemical transitions probed by Raman spectroscopy. Often, this fluorescence background and its natural variability make biochemical analysis using Raman spectroscopy impractical. In this work, we present the theory and the implementation of an innovative modulated Raman spectroscopy technique to filter out the Raman spectra from the fluorescence background by modulating of the excitation wavelength. The method is based on the continuous wavelength shift of the Raman peaks with the modulation of the laser wavelength while the fluorescence background remains static. Exploiting this physical property allows us to clearly distinguish between the Raman signal and the fluorescence background. Our method is related to wavelength shifting Raman spectroscopy but incorporates two key novel elements: (i) the use of more than two excitation wavelengths and (ii) multi-channel lock-in detection of the Raman signal for suppression of the fluorescence background. Our results establish a direct and practical approach for fluorescence background suppression in 'real-time' Raman spectroscopy for in-vivo biomedical applications.