This paper presents a gain invariant speech watermarking technique based on quantization of the Lp-norm. In this scheme, first, the original speech signal is divided into different frames. Second, each frame is divided into two vectors based on odd and even indices. Third, quantization index modulation (QIM) is used to embed the watermark bits into the ratio of the Lp-norm between the odd and even indices. Finally, the Lagrange optimization technique is applied to minimize the embedding distortion. By applying a statistical analytical approach, the embedding distortion and error probability are estimated. Experimental results not only confirm the accuracy of the driven statistical analytical approach but also prove the robustness of the proposed technique against common signal processing attacks.