Logarithmic Quantization Index Modulation (LQIM) is an important extension of the original quantization-based watermarking method. However, it is well known that it is sensitive to valumetric scaling attack and easy to result in sign error after quantization and attacks. For that, in this paper, we propose a new method, namely Logarithmic Spread-Transform Dither Modulation Based on Perceptual Model (LSTDM-WM). In this regard the host signal is first projected onto a random vector and transformed using a novel Logarithmic Quantization function. Then the transformed signal is quantized regarding the watermark data and the watermarked signal is obtained by applying inverse transform to the quantized signal. The perceptual model is further exploited to adjust the quantization step adaptively for watermark embedding. Experimental results indicate that our proposed scheme overcomes two challenges cited above and has superior performance in comparison with conventional LQIM and former proposed schemes of STDM.