Airborne radar with uniform circular array (UCA) antennas has the merits of all-orientation space scanning, joint elevation-azimuth estimation, and good beamform when the beam center deviates from the normal of the array. But the clutter distribution of UCA varied with ranges and received data in different range cells are not independently identically distributed (IID) samples for its geometry specialty, which results in the significant degradation in traditional space time adaptive processing (STAP) method. A new STAP method, namely exponent derivative based updating algorithm, is proposed. In the method, the change of adaptive weight is supposed as an exponential function and the range-dependency of UCA can be effectively reduced by extending the received data vectors. Simulation results verify that the proposed method outperforms significantly both localized processing and range-dependency compensation methods, as well as the traditional derivative-based updating algorithm.