We developed a tip-enhanced Raman spectrometer (TERS) with reflection mode. The instrument, with a scanning shear-force microscope (ShFM) and a side-illumination Raman spectroscope, can overcome the diffraction limit and has high sensitivity. A chemical method to fabricate optical fiber probes with Ag coating is proposed. The local electromagnetic responses of the silver-coated optical fiber probe are numerically analyzed by the finite-difference time-domain method, and the excitation wavelength is optimized to resonate with the localized surface plasmons (LSP) of the probe tip. The instrument is applied to investigate a single multiwall carbon nanotube. The experiment results indicate that our TERS instrument has a spatial resolution better than $70\mathrm{nm}$ , and the enhancement factor is about $5\times {10}^3$ .