Space-time adaptive processing (STAP) is a well-suited technique to detect the slow-moving target in the presence of a clutter-spreading environment. When considering the airborne radar deployed with conformal array (CFA), the statistics of the secondary data snapshots used to estimate the optimum weight vector are not identically distributed with respect to range, thus preventing the STAP processor from achieving its optimum performance. In order to compensate the clutter range dependence problem induced by geometry with CFA, a two-stage hybrid clutter range dependence compensation method is proposed, which can compensate the clutter range dependence problem in mainlobe as well as in sidelobe. This method first compensate the mainlobe clutter spectrum in different range bins by a pre-processing procedure with angle-Doppler compensation (ADC) method, and subsequently compensate the sidelobe clutter spectrum with modification derivative based update (MDBU) method. Simulation results show that the proposed method outperforms the conventional compensation methods and can improve the STAP performance dramatically.