Summary: We propose a characteristic centred finite difference method on non-uniform grids to solve the problem of an air pollution model. Numerical solutions and error estimates of air pollution concentration and its first-order derivatives for space variables are obtained. The computational cost of the method is the same as that of the characteristic difference method based on a linear interpolation. The error order of the numerical solutions is the same as that of the characteristic difference method based on a quadratic interpolation. At last, we give numerical examples to illustrate feasibility and efficiency of this method.