This paper studies the problem of principal-agent with moral hazard in continuous time.The firm\'s cash flow is described by geometric Brownian motion(hereafter GBM).The agent affects the drift of the firm\'s cash flow by her hidden effort.Meanwhile,the firm rewards the agent with corresponding compensation and equity which depend on the output.The model extends dynamic optimal contract theory to an inflation environment.Firstly,the authors obtain the dynamic equation of the firm\'s real cash flow under inflation by using the Ito formula.Then,the authors use the martingale representation theorem to obtain agent\'s continuation value process.Moreover,the authors derive the Hamilton-Jacobi-Bellman(HJB)equation of investor\'s value process,from which the authors derive the investors\'scaled value function by solving the second-order ordinary differential equation.Comparing with He[1],the authors find that inflation risk affects the agent\'s optimal compensation depending on the firm\'s position in the market.