We investigate the Airy–Talbot effect of an Airy pulse train in time-dependent linear potentials. The parabolic trajectory of self-imaging depends on both the dispersion sign and the linear potential gradient. By imposing linear phase modulations on the pulse train, the Airy–Talbot effects accompanied with positive and negative refractions are realized. For an input composed of stationary Airy pulses, the self-imaging follows straight lines, and the Airy–Talbot distance can be engineered by varying the linear potential gradient. The effect is also achieved in symmetric linear potentials. The study provides opportunities to control the self-imaging of aperiodic optical fields in time dimension.