Considering the time-delay characteristics of input-output systems, a GDM(1,2) model is established. Combining the cubic spline interpolation with the particle swarm optimization(PSO), the parameters［a,b,τ］of the model are obtained by the intelligent optimization algorithm. Compared with the traditional method in which the grey relational model is used to estimate the time-delayτbefore solving the grey prediction model, this method can avoid the error transfer in the process of solving parameters and remove the limitation that time-delayτmust be an integer, which is more fit to the actual. Then parameters are substituted into time response formula to conclude the solution of the model. Finally，the model is applied to the prediction of highway passenger turnover in China. Result shows that the model has high accuracy in input-output systems with time-delay characteristics.