Due to large data set, block processing is usually applied for fast compressive sensing (CS) reconstruction; however, it gives the undesired blocking artifact in reconstructed data. In order to reduce blocking artifact and preserve high frequency, this paper proposes a novel block processing on wavelet domain instead of spatial domain. No post-processing nor special mapping is included. CS is applied only on blocks where the data are really sparse. An enhancing process, often included for artifact reduction, is no longer necessary. Our algorithm was evaluated by reconstructing three standard images (Lena, Mandrill and Peppers) and then compared with scrambled block hadamard ensemble (SBHE) and block-based CS sampling with a smoothed PL variant using directional discrete wavelet transform (BCS-SPL-DDWT). In the experiment, it provided better reconstruction both objectively (PSNR) and subjectively at low measurement rate. It gave the sharpest image in all cases. Details were preserved and blocking artifact was not detectable.