High false-positive (FP) rate remains to be one of the major problems to be solved in CAD study because too many false-positively cued signals will potentially degrade the performance of detecting true-positive regions and increase the call-back rate in CAD environment. In this paper, we proposed a novel classification method for FP reduction, where the conventional "hard" decision classifier is cascaded with a "soft" decision classification with the objective to reduce false-positives in the cases with multiple FPs retained after the "hard" decision classification. The "soft" classification takes a competitive classification strategy in which only the "best" ones are selected from the pre-classified suspicious regions as the true mass in each case. A neural network structure is designed to implement the proposed competitive classification. Comparative studies of FP reduction on a database of 79 images by a "hard" decision classification and a combined "hard"-"soft" classification method demonstrated the efficiency of the proposed classification strategy. For example, for the high FP sub-database which has only 31.7% of total images but accounts for 63.5% of whole FPs generated in single "hard" classification, the FPs can be reduced for 56% (from 8.36 to 3.72 per image) by using the proposed method at the cost of 1% TP loss (from 69% to 68%) in whole database, while it can only be reduced for 27% (from 8.36 to 6.08 per image) by simply increasing the threshold of "hard" classifier with a cost of TP loss as high as 14% (from 69% to 55%). On the average in whole database, the FP reduction by hybrid "hard"-"soft" classification is 1.58 per image as compared to 1.11 by "hard" classification at the TP costs described above. Because the cases with high dense tissue are of higher risk of cancer incidence and false-negative detection in mammogram screening, and usually generate more FPs in CAD detection, the method proposed in this paper will be very helpful in improving the performance of early detection of breast cancer with CAD.