In accordance with the detection of small targets in an infrared image, an adaptive clutter suppression method based on image sparse representation was proposed. First, 500 frames of infrared images were sampled, and an over complete and multi-component dictionary containing characteristics of every image layers was constructed through learning and training. Then, the over complete dictionary corresponding to the image subblock was selected adaptively to represent the image sparsely through the covariance of the infrared image, and the optimum representative coefficients of the subimage under the over-complete target dictionary were obtained through matching the tracking algorithm. Finally, the image subblock was reconstructed according to the representative coefficients and the corresponding atomic vector and the high SNR reconstructed image which protruded the infrared small targets were acquired, and the clutter was suppressed. Many experiments under different circumstances indicate that the algorithm proposed in this paper can suppress the clutter under complex backgrounds and can raise the SNR. The target and background can be separated through simple threshold division, which lays foundation for the target detection process that follows up. Obtained results show that the method has smaller computation costs, stronger robustness and is easy to be realized by hardware.