This paper presents a fast block-matching algorithm based on the normalized cross-correlation, where the elimination order is determined based on the gradient magnitudes of subblocks in the current macroblock. Multilevel Cauchy-Schwartz inequality is derived to skip unnecessary block-matching calculations in the proposed algorithm. Also, additional complexity reduction is achieved re-using the normalized cross correlation values for the spatially neighboring macroblock because the search areas of adjacent macroblocks are overlapped. Simulation results show that the proposed algorithm can improve the speed-up ratio up to about 3 times in comparison with the existing algorithm.