The collision integral cross-sections of double-photon Compton process are measured experimentally for 662keV incident gamma photons. The measurements are successfully carried out using a single gamma ray detector, and do not require the complicated slow-fast coincidence technique used till now for observing this higher order quantum electrodynamics (QED) process. The energy spectra of one of the two final photons, originating in this process, in direction of the gamma ray detector are observed as a long tail to the single-photon Compton line on lower side of the full energy peak in the observed spectra. An inverse response matrix converts the observed pulse-height distribution of a NaI(Tl) scintillation detector to a true photon spectrum. This also results in extraction of events originating from double-photon Compton interactions. The present measured values of collision integral cross-section, although of same magnitude, deviate from the corresponding values obtained from the theory. In view of the magnitude of deviations, in addition to small value of probability of occurrence of this process, the agreement of measured values with theory is reasonably acceptable.