A low-cost near-infrared spectrometer based on fiber beam scanning and linear variable filter (LVF) was proposed and demonstrated. The key elements of the spectrometer include a piezoelectric driven fiber scanner, an LVF monochromator, and a single point detector. The single fiber scanner provides a new way to continuously sweep the LVF. A PIN photodiode behind the LVF monochromator can acquire more spectral information than the traditional linear array detection. The performance of the spectrometer was verified with a narrow band tunable laser and a broadband light source. With the help of a deconvolution algorithm, the spectral resolution of the proposed spectrometer is up to 0.32% of the center wavelength (≈5  nm@1550  nm).