Attribute reduction is a core issue in formal concept analysis(FCA). Of all attribute reduction approaches, the ones based on discernibility matrix and discernibility function are of most importance. However, in the traditional discernibility matrices, the comparisons between every two concepts result in a high computation complexity: O(nl2). Therefore, an object-concept discernibility matrix is constructed to obtain the reducts of the incomplete contexts, and the computation complexity is reduced to O(mnl). In most cases, m is much smaller than l, so O(mnl) ? O(nl2). The partial order of the concept lattice is further used to simplify the object-concept discernibility matrix. Theoretical analysis and experimental results show the effectiveness of the proposed methods.