A table-top near-edge X-ray absorption fine structure (NEXAFS) spectroscopy system consisting of a soft X-ray source and an integrated spectrometer with a significantly improved resolution is presented. The soft X-ray source is based on a long-term stable and nearly debris-free picosecond laser-induced plasma generated in a pulsed krypton gas jet target. Photon energies ranging from 250 to 1000 eV can be used for the absorption spectroscopy of thin samples. The newly designed spectrometer accomplishes a spectral resolution of E/ΔE = 1535 at 430 eV, being close to typical synchrotron setups. Moreover, a simultaneous multi-edge analysis is possible. The performance of the new system is demonstrated by investigating the fine structure of the K- and L-absorption edges of various elements (carbon, calcium, oxygen, iron, nickel, and copper) for different types of samples. An excellent agreement with synchrotron spectra is achieved.