Block Truncation Coding (BTC), using a one-bit moment preservign quantizer to quantize a block, is a simple compression method; however, compressin with BTC cannot be used to obtain a sufficiently high quality image, especially an image with many edges. In this paper, a new generalized multilevel BTC algorithm, which arbitrarily specifies the nubmer of quantization levels, is developed. In the proposed algorithm, a nearly optimum quantizer is proposed based on a multiplication-free and non-exhaustive search such that the computation complexity is very low. The simulation results indicate that both the computation complexity and the reconstructed image quality obtained using the proposed multilevel BTC algorithm are better than those obtainable with other existing multilevel BTC algorithms.