The cost control goal of the construction project manager is to meet the requirement of cost control and improve the efficiency of cost control through the incentive contract. But it is incomplete that managers use the incentive mechanism to control the cost of unit product without considering the time and energy of workers spent to improve the efficiency of cost control, which affects their benefit and enthusiasm of reducing the cost of production. Thus a dynamic cost game is formed between managers and workers around the profit distribution generated by reduction of product cost. This paper proposes a principal-agent model based on unit time under the background of construction project. It is found that the level of workers' effort has nonlinear positive correlation with the incentive ratio; the workers' profit will increase to the peak firstly and then decrease with the increases of workers' effort level in a certain range; when the level of workers' effort is optimal, the managers' profit increase to the peak with the increase of incentive ratio. By setting a reasonable incentive ratio, managers and workers can achieve the maximum profit. Finally, the feasibility of the model is analyzed with the example of rebar making and bonding process.