The rapidly growing ultrafast science with X-ray lasers unveils atomic scale processes with unprecedented time resolution bringing the so called "molecular movie" within reach. X-ray absorption spectroscopy is one of the most powerful x-ray techniques providing both local atomic order and electronic structure when coupled with ad-hoc theory. Collecting absorption spectra within few x-ray pulses is possible only in a dispersive setup. We demonstrate ultrafast time-resolved measurements of the LIII-edge x-ray absorption near-edge spectra of irreversibly laser excited Molybdenum using an average of only few x-ray pulses with a signal to noise ratio limited only by the saturation level of the detector. The simplicity of the experimental set-up makes this technique versatile and applicable for a wide range of pump-probe experiments, particularly in the case of non-reversible processes.