A highly efficient Graphics Processing Unit(GPU) based method for decomposing SAR azimuth signal is presented. SAR azimuth signal is decomposed by the four-parameter Chirplet decomposition method. This method needs excessive computation mainly to construct Chirp atomic dictionary and decompose SAR azimuth signal in the over-complete dictionary. Compared with CPU, GPU is well suited for data parallel computations with high arithmetic intensity. A new method is introduced that takes full advantage of GPU’s computation capability by transferring the key part of the algorithm to GPU.The experimental results shows that this method is more than ten times as fast as traditional CPU based algorithms.