The purpose of image compression is to store or transmit image data efficiently. However, most compression methods emphasize the compression ratio rather than the throughput. We propose an encoding process and rules, and consequently a fast-adaptive near-lossless image compression method (FAIC) with good compression ratio. FAIC is a single-pass method, which removes bits from each codeword, then predicts the next pixel value through localized edge detection techniques, and finally uses Golomb–Rice codes to encode the residuals. FAIC uses only logical operations, bitwise operations, additions, and subtractions. Meanwhile, it eliminates the slow operations (e.g., multiplication, division, and logarithm) and the complex entropy coder, which can be a bottleneck in hardware implementations. Besides, FAIC does not depend on any precomputed tables or parameters. Experimental results demonstrate that FAIC achieves good balance between compression ratio and computational complexity in certain range (e.g., peak signal-to-noise ratio <35 dB, bits per pixel<2). It is suitable for applications in which the amount of data is huge or the computation power is limited.