In this paper, a logarithmic adaptive quantization projection (LAQP) algorithm for digital watermarking is proposed. Conventional quantization index modulation uses a fixed quantization step in the watermarking embedding procedure, which leads to poor fidelity. Moreover, the conventional methods are sensitive to value-metric scaling attack. The LAQP method combines the quantization projection scheme with a perceptual model. In comparison to some conventional quantization methods with a perceptual model, the LAQP only needs to calculate the perceptual model in the embedding procedure, avoiding the decoding errors introduced by the difference of the perceptual model used in the embedding and decoding procedure. Experimental results show that the proposed watermarking scheme keeps a better fidelity and is robust against the common signal processing attack. More importantly, the proposed scheme is invariant to value-metric scaling attack.