Modulation recognition is an important technology used to correctly identify the modulation modes of wireless signals and is widely used in cooperative and confrontational scenarios. Traditional modulation-recognition algorithms require the assistance of expert experiences, which constrains their applications. With the rapid development of artificial intelligence in recent years, deep learning (DL) is widely advocated for intelligent modulation recognition. Typically, DL-based modulation-recognition algorithms implicitly assume a relatively static scenario in which the signal samples of all the modulation modes can be completely collected in advance. In practical situations, the radio environment is quite dynamic and the signal samples with new modulation modes may appear sequentially, in which the current DL-based modulation-recognition algorithms may require unacceptable time and computing resource consumption to re-train the optimal model from scratch. In this study, we leveraged incremental learning (IL) and designed a novel IL-based modulation-recognition algorithm that consists of an initial stage and multiple incremental stages. The main novelty of the proposed algorithm lies in the new loss function design in each incremental stage, which combines the distillation loss of recognizing old modulation modes and the cross-entropy loss of recognizing new modulation modes. With the proposed algorithm, the knowledge of the signal samples with new modulation modes can be efficiently learned in the current stage without forgetting the knowledge learned in the previous stages. The simulation results demonstrate that the proposed algorithm could achieve a recognition accuracy close to the upper bound with a much lower computing time and it outperformed the existing IL-based benchmarks.