A Princeton Instruments PI-LCX 1300 charge-coupled device (CCD) camera used for X-ray spectrum measurements in laser-plasma experiments is calibrated using three radioactive sources and investigated with the Monte Carlo code Geant4. The exposure level is controlled to make the CCD work in single photon counting mode. A summation algorithm for obtaining accurate X-ray spectra is developed to reconstruct the X-ray spectra, and the results show that the developed algorithm effectively reduces the low-energy tail caused by split pixel events. The obtained CCD energy response shows good linearity. The detection efficiency curves from both Monte Carlo simulations and the manufacturer agree well with the experimental results. This consistency demonstrates that event losses in charge collection processes are negligible when the developed summation algorithm of split pixel events is employed.