This paper analyzes how to achieve the cost-effectiveness by initial allocation of CO2 emission permits when a single dominant firm in production market has market power in auction, and compare two prevalent allocation patterns, mixed allocation and single auction. We show how the firm with market power may manipulate the auction price, thereby this leads to fail to achieve cost-effective solution by auction unless the total permits for allocation equal to the effective emissions cap. Provided that the market power firm receives strictly positive free permits, the effective emissions cap of mixed allocation is larger than that of single auction. The production market share of dominant firm is increasing with the free permits it holds. Finally, we examine the compliance costs and welfare of mixed allocation and single auction, the result show that the former is preferred to the later when policy makers consider economic welfare without welfare cost due to CO2 emissions.