Synthetic aperture radar (SAR) is a device for observing the ground surface and is one of the important technologies in the field of microwave remote sensing. In SAR observation, a platform equipped with a small-aperture antenna flies in a straight line and continuously radiates pulse waves to the ground during the flight. After that, by synthesizing the series of observation data obtained during the flight, one realize high-resolution ground surface observation. In SAR observation, there are two spatial resolutions defined in the range and azimuth directions and they are limited by the bandwidth of the SAR system. The purpose of this study is to improve the resolution of SAR by sparse reconstruction. In particular, we aim to improve the resolution of SAR without changing the frequency parameters. In this paper, we propose to improve the resolution of SAR using the deconvolution iterative shrinkage-thresholding algorithm (ISTA) and verify the proposed method by carrying out an experimental analysis using an actual SAR dataset. Experimental results show that the proposed method can improve the resolution of SAR with low computational complexity.