Audio watermarking is a promising technique for copyright protection of audio data. However, the existing audio watermarking algorithms cannot satisfy requirements on imperceptibility, embedding capacity, and robustness, especially against desynchronization attacks, such as cropping, jittering, and time-scale modification. This paper proposes a novel audio watermarking algorithm, LIPAS, based on local invariant points and adaptive embedding strength. Specifically, we consider one feature robust to desynchronization attacks, i.e., local invariant points, and use these invariant points as positional references for the embedding regions. Next, an adaptive embedding strength strategy is proposed to enhance the imperceptibility of the watermark and ensure robustness. In addition, the watermarks are embedded into the audio vectors using a polarity adjustment method. The effectiveness, imperceptibility, and robustness of the LIPAS algorithm were demonstrated in the experiments.