In line with the development of Synthetic Aperture Radar (SAR) technology, there is a serious problem when the SAR signal is acquired using high rate analog digital converter (ADC), that require large volumes data storage. The other problem on compressive sensing method,which frequently occurs, is a large measurement matrix that may cause intensive calculation. In this paper, a new approach was proposed, particularly on the partial acquisition technique of SAR system using compressive sampling method in both the azimuth and range direction. The main objectives of the study are to reduce the radar raw data by decreasing the sampling rate of ADC and to reduce the computational load by decreasing the dimension of the measurement matrix. The simulation results found that the reconstruction of SAR image using partial acquisition model has better resolution compared to the conventional method (Range Doppler Algorithm/RDA). On a target of a ship, that represents a low-level sparsity, a good reconstruction image could be achieved from a fewer number measurement. The study concludes that the method may speed up the computation time by a factor 4.49 times faster than with a full acquisition matrix.