Existing association-rule mining algorithms mainly rely on the support-based pruning strategy to prune its combinatorial search space. This strategy is not quite effective in the process of mining potentially interesting low-support patterns. To solve this problem, the paper presents a novel concept of association pattern called credible association rule (CAR), in which each item has the same support level. The confidence directly reflects the credible degree of the rule instead of the traditional support. This paper also proposes a MaxCliqueMining algorithm which creates 2-item credible sets by adjacency matrix and then generates all rules based on maximum clique. Some propositions are verified and which show the properties of CAR and the feasibility and validity of the algorithm. Experimental results on the alarm dataset and Pumsb dataset demonstrate the effectiveness and accuracy of this method for finding CAR.