This paper reports on the demonstration of a high-rate energy measurement technique using a thin depletion layer silicon avalanche photodiode (Si-APD). A dedicated amplitude-to-time converter is developed to realize simultaneous energy and timing measurement in a high rate condition. The energy response of the system is systematically studied by using monochromatic X-ray beam with an incident energy ranging from 6 to 33 keV. The obtained energy spectra contain clear peaks and tail distributions. The peak fraction monotonously decreases as the incident photon energy increases. This phenomenon can be explained by considering the distribution of the energy deposit in silicon, which is investigated by using a Monte Carlo simulation.