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The characteristics of clutter nonstationarity for airborne radar with conformal antennas array (CAA) are analyzed, and an improved angle-Doppler compensation method is proposed based on above analysis. Unlike the uniform linear antennas array (LAA), the elements of CAA distribute in three-dimension space which lead to that the clutter angle-Doppler spectrum distribution should be described in four-dimension space. According to this theory, the clutter nonstationarity for airborne radar with CAA is firstly analyzed and the nonstationary nature of it is given. Then an improved STAP method for airborne radar with CAA which compensates the mainlobe clutter in four-dimension frequency domain is proposed. Finally, the simulation shows the effectiveness of the novel method for clutter suppression in airborne radar with CAA.