Carbon emission is generally viewed as the main cause of climate change. A lot of policies have been presented to control carbon emission all over the world. In this paper, a simple optimization model is developed to demonstrate that carbon emission constraint will restrain the firm from increasing its production under command-and-control regulation, which presents a motivation for the firm to break the command-and-control regulation. Then based on a game theory model between the regulator and the firm, we find that there are several factors which will impact their strategy about carbon emission abatement. Finally, some policy implications are presented to enhance climate policy efficiency.