This paper presents a novel block-based fast compression (BFC) algorithm for compound images that contain graphics, text and natural images. The images are divided to blocks, which are classified into four different types - smooth blocks, text blocks, hybrid blocks and picture blocks with a fast and effective block-based classification algorithm. Four different coding algorithms are carefully designed for each block type according to their different statistical properties to maximize the compression performance. Simulations show that the BFC algorithm we propose has much lower complexity than DjVu with significant better visual quality at high bit rate, and it also outperforms the popular lossy image coding method JPEG.