In well logging, large amounts of data need to be sent from downhole to the surface by means of a very band-limited telemetry system. The limited bandwidth usually results in prolonging of expensive rig time and/or the sacrifice of borehole information. Data compression techniques, to some extent, may relieve this problem. We deduced the adaptive (4, 4) lifting integer-to-integer wavelet transform formula and its inverse transform formula based on the basic principle of wavelet transform, and we explored an appropriate bit-recombination mark coding approach according to the characteristics of wavelet transform coefficients. Then a new lossless compression method for acoustic waveform data based on wavelet transform and bit-recombination mark coding was discovered. The compression method mainly consists of wavelet transform, data type conversion, bit-recombination, and mark coding, whereas the decompression method consists of mark decoding, bit-recovery, data type conversion, and inverse wavelet transform. The compression and decompression programs were developed according to the proposed method. Compression and decompression tests were then applied to field and synthetic acoustic logging waveform data, and the compression performance of our method and several other lossless compression methods were compared and analyzed. Test results validated the correctness of our method and demonstrated its advantages. The new method is potentially applicable to acoustic waveform data compression.