Aiming to the question that geometric attacks desynchronize watermark detection to fail many watermark schemes, we present a new geometrically robust image watermarking scheme based on Tchebichef moments (GWTM). Geometric distortions are first resynchronized by image normalization, and watermark insertion and extraction are implemented in normalized domain. To select a moment set fits watermark embedding using the property of Tchebichef moments. According to the magnitude changes of the above moment set after being modified, an optimal moment set is determined by test, and the moments within it are modified according to the random watermark bits. The modified optimal moment set is reconstructed to obtain the watermarked image. In detection, the watermark bits are extracted by comparing with the Tchebichef moments of original image with the optimal moment set as a key. Experimental results show that GWTM can efficiently resist rotation attacks of random angles, scaling attacks and common signal processing attacks.