As to the modeling problems in small sample systems with time-delay causality, the multivariable grey time-delay GM(1,N) model and its solving method are proposed. Considering that driving items in the model can not be seen as grey constants when the accumulative sequences of relevant variables change significantly, a derived GM(1,N) model with timedelay is further deduced. On this basis, the effectiveness of the new model is verified by the numerical simulation and actual examples. Results show that the time-delay GM(1,N) model can better describe and predict delay characteristics of systems with small sample data. The time-delay GM(1,N) model degenerates to the traditional one without considering the factor of time-delay.