This study presents an optimization-based image watermarking scheme that applies summation quantization technique to multi-coefficients of discrete wavelet transform (DWT). Peak signal-to-noise ratio (PSNR) and bit error ratio (BER) are commonly performance indexes in measuring the quality and robustness of an image watermarking scheme. To optimize the tradeoff between PSNR and BER, we minimize the difference between original and watermarked frequency coefficients. First, PSNR is expressed as a performance index using matrix form. Then, an optimized-quality functional that relates the performance index to the summation quantization technique is obtained. Finally, the Lagrange Principle is utilized to obtain the optimal solution. The optimal solution is applied to watermarking. Experimental results show that the watermarked image can keep high PSNR and achieve better BER even when the number of coefficients for embedding a watermark bit increases.