After extensive study on the small-world and scale-free properties of networks, the research focus is shifting to detailed local structures. Empirical analysis shows that many real networks exhibit the power-law clique-degree distribution. This general regularity cannot be produced by the rich-get-richer mechanism. In this paper, we propose a common-neighborhood-dirven model in which the observed power-law clique-degree distribution con be well reproduced, indicating that the common-neighborhood-dirven mechanism is an essential factor leading to the emergence of local structures.