The propagation of three-dimensional controllably accelerating and decelerating Airy-elegant-Laguerre–Gaussian (CAiELG) wave packets in free space is investigated theoretically and numerically by solving the Schrödinger equation in cylindric coordinates. The CAiELG wave packets are constructed with the Airy pulses with the initial velocity in temporal domain and the elegant-Laguerre–Gaussian beams in space domain. Decelerating and accelerating AiELG wave packets are obtained by selecting different initial velocities. The initial velocities can be determined by incident angle and directions. According to the intensity distribution of CAiELG wave packets at the propagating section, two special types of wave packets are accessed: one type is ring shaped with the modulation depth and another type is necklace shaped with . The direction of the energy flow of CAiELG wave packets is kept away from the center during propagation, and their Poynting vector snapshots at different propagating distances are shown.