Raman spectroscopy has been used as a sensitive tool for studying biological tissue and evaluating disease. In many applications, microscopic level resolution spectral analysis is desirable. And this has been performed mostly by expensive commercial confocal micro-Raman systems. In this research, we present a simple method for building an economical and modular Raman microspectroscopy system that combines a microscope with a Raman spectrometer using an optical fiber bundle. The bundle with a circular collection end is positioned at an image plane of the microscope to collect Raman signals from the interested micro-location on the sample. The light delivery end is specially configured so that its 37 fibers are arranged along a straight line to fit into the spectrometer entrance slit. This configuration improves light collection efficiency and maintains high spectral resolution. To battle the great background autofluorescence and Raman signals that could originate from the microscope slides and optics due to the non-confocal set-up of our simplified system, conventional normal-incident illumination is replaced by oblique illumination at 45° degrees and the microscope slides are coated with gold. We demonstrated the usefulness of the system by measuring micro-Raman spectra from different skin layers on vertical sections of normal skin tissue samples.