This paper introduces a new modified Lee–Carter model for analysing short-base-period mortality data, for which the original Lee–Carter model produces severely fluctuating predicted age-specific mortality. Approximating the unknown parameters in the modified model by linearized cubic splines and other additive functions, the model can be simplified into a logistic regression when fitted to binomial data. The expected death rate estimated from the modified model is smooth, not only over ages but also over years. The analysis of mortality data in China (2000–08) demonstrates the advantages of the new model over existing models.