With the tremendous amount of images distributed over Internet, image authentication has drawn extensive attention for integrity verification. For instance, watermarking fragile to malicious modifications while robust to data compression has been proposed for image authentication. However, the security of watermark has not received enough attention yet. In this paper, we propose a secure semi-fragile watermarking scheme for image authentication based on integer wavelet transform with parameters. The features of the proposed scheme are as follows. Firstly, parameterized integer wavelet transform is adopted. The wavelet base is chosen by a parameter. It is impossible to extract the watermark without the exact parameter and thus the security of the watermark is guaranteed. Secondly, the performance of the generated watermark is improved and the computational complexity is reduced due to the lifting scheme used in the proposed framework of parameterized integer wavelet transform. Thirdly, the proposed watermark can tolerate JPEG lossy compression to a quality factor as low as 40, while being sensitive to malicious attack and able to locate the tampered area accurately. Experimental results demonstrate the merits of the proposed algorithm.