In this paper,an Entropy-constrained dictionary learning algorithm(ECDLA) is introduced for efficient compression of Synthetic aperture radar(SAR) complex images.ECDLA RI encodes the Real and imaginary parts of the images using ECDLA and sparse representation,and ECDLA AP encodes the Amplitude and phase parts respectively.When compared with the compression method based on the traditional Dictionary learning algorithm(DLA),ECDLA RI improves the Signal-to-noise ratio(SNR) up to 0.66 dB and reduces the Mean phase error(MPE) up to 0.0735 than DLA RI.With the same MPE,ECDLA AP outperforms DLA AP by up to 0.87 dB in SNR.Furthermore,the proposed method is also suitable for real-time applications. In this paper, an Entropy-constrained dictionary learning algorithm (ECDLA) is introduced for efficient compression of Synthetic Aperture Radar (SAR) complex images. ECDLA RI encodes the Real and imaginary parts of the images using ECDLA and sparse representation, and ECDLA AP encodes the Amplitude and phase parts respectively. Comparison with the compression method based on the traditional Dictionary learning algorithm (DLA), ECDLA RI improves the Signal-to-noise ratio (SNR) up to 0.66 dB and reduces the Mean phase error (MPE) up to 0.0735 than DLA RI. The same MPE, ECDLA AP outperforms DLA AP by up to 0.87 dB in SNR. Still further, the proposed method is also suitable for real-time applications.