We demonstrate an ultra-compact, broadband on-chip near-infrared (NIR) spectroscopy system based on a narrow-band plasmonic filter array. The entire filter array, consisting of 28 individual subwavelength metallic gratings, was monolithically integrated in a thin gold film on a quartz substrate, covering a 270 nm spectra from 1510 nm to 1780 nm. In order to achieve a high spectral resolution, extremely narrow slits are created for the gratings with a polymer waveguide layer on top, generating narrow-band guided-mode resonances through coupling with the surface-plasmon resonances of the metallic gratings. Experimental results show that the transmission bands of the filter array have full width at half-maximum of only 7 nm-13 nm, which is sufficient for NIR spectroscopy. The NIR absorption spectroscopy of xylene using the on-chip plasmonic filter array matches very well with the results from conventional Fourier transform infrared spectroscopy, which proves the great potential for NIR sensing applications.