A laser driven electron x-ray source (LEXS) emitting tungsten Lα lines has been built based on a high repetition rate, terawatt laser system. The Lα characteristic lines overlap with the absorption edge of Ni near 8333 eV. Using this x-ray source, the x-ray absorption spectra near the absorption edge of different Ni compounds have been measured. We term this new method "ultrafast selected energy x-ray absorption spectroscopy (USEXAS)." It provides an efficient way to study ultrafast reaction dynamics of many metal complexes in solution.