For the first order reaction on a fractal surface, the reaction rate constant is assumed to be time dependent, and the kinetic expression takes the form: C_A=C_(A0) exp (-k’t~(2/d)), where k’ is a constant and d_w is the fractal dimension of the trajectory. For two types of fractals, Sierpinski gasket and percolation cluster, Monte Carlo simulations show that the expression can effectively describe the kinetics of the first order reaction on the fractals. For the first order reaction on a fractal surface, the reaction rate constant is assumed to be time dependent, and the kinetic expression takes the form: C_A = C_ (A0) exp (-k’t ~ (2 / d)), where k ’is a constant and d_w is the fractal dimension of the trajectory. For two types of fractals, Sierpinski gasket and percolation cluster, Monte Carlo simulations show that the expression can effectively describe the kinetics of the first order reaction on the fractals.