The task of outlier detection is to find small groups of data objects that are exceptional when compared with rest large amount of data. Recently, the problem of outlier detection in categorical data is defined as an optimization problem and a local-search heuristic based algorithm (LSA) is presented. However, as is the case with most iterative type algorithms, the LSA algorithm is still very time-consuming on very large datasets. In this paper, we present a very fast greedy algorithm for mining outliers under the same optimization model. Experimental results on real datasets and large synthetic datasets show that: (1) Our new algorithm has comparable performance with respect to those state-of-the-art outlier detection algorithms on identifying true outliers and (2) Our algorithm can be an order of magnitude faster than LSA algorithm.