According to the compressive sensing theory, it is possible to perfectly reconstruct a signal only with a fewer number of measurements than the Nyquist sampling rate if the signal is a sparse signal which satisfies a few related conditions. From practical viewpoint for image applications, it is important to reduce its computational complexity and memory burden required in reconstruction. In this regard, a Block-based Compressive Sensing (BCS) scheme with Smooth Projected Landweber (BCS-SPL) has been already introduced. However, it still has the computational complexity problem in reconstruction. In this paper, we propose a method which modifies its stopping criterion, tolerance, and convergence control to make it converge faster. Experimental results show that the proposed method requires less iterations but achieves better quality of reconstructed image than the conventional BCS-SPL.