Direct measurement of mammographic X-ray spectra under clinical conditions can be useful for quality control (QC) in mammography for estimating image quality and patient dose. The measurement of mammographic X-ray spectra using the traditional detectors with multi-channel pulse height analyzer (MCA) systems is challenging because of the limitations imposed on measurements with high energy resolution at high photon counting rates, as well as geometrical restrictions, especially in a hospital environment. Semiconductor photon-counting detectors equipped with faster electronics enable utilization in somewhat high count rate situations at the expense of decreased energy resolution. This work presents a method for estimating mammography X-ray spectra from measurements acquired with a multi-energy bin photon counting detector. Simulation tests were conducted out for different incident X-ray spectra, energy thresholds and for multiple noise realizations assuming an ideal photon-counting X-ray detector with three energy thresholds. In addition, experimental measurements of mammography X-ray spectra were estimated by using a high-count rate Gallium Arsenide (GaAs) photon counting detector (with two or four energy thresholds) and a high resolution X-ray spectroscopy detector with Cadmium Telluride (CdTe) sensor for comparison. Differences between half-value layer values (HVL) obtained from the estimated spectra using the proposed method were found to be within 0.04 mm of the true values. This proposed method could be an attractive tool for laboratory research and calibration of photon-counting detectors.