Dendrite growth during solidification of an IN718 alloy under forced convection induced by ultrasonication was simulated via the coupled cellular automaton–lattice Boltzmann (CA–LB) model. To demonstrate the validity of the LB modeling of ultrasonic propagation, the LB simulation results of acoustic attenuation in the melt are well compared with those of an analytical model reported in the literature. The CA–LB model was then used to simulate the growth of equiaxed and columnar dendrites under different ultrasonic amplitudes in the nonequilibrium solidification process. The simulation results revealed that the presence of ultrasound drastically influenced the solute concentration field in the liquid. The distribution of liquid concentrations accelerated the growth of dendrite arms near the sound source but repressed the growth of those far from the sound source. For multiple equiaxed dendrites, the average liquid concentration was relatively low at the initial stage without ultrasonication, whereas the average liquid concentration at the end stage was relatively high. Ultrasound accelerated the growth rate of a portion of the columnar dendrites near the sound source, which influenced their competitive growth mode and affected the final morphology. The present work not only reproduced the morphological evolution of different types of dendrites under ultrasound effects but also revealed the complex interactions among ultrasound-induced convections, the solute concentration field, and the kinetics of dendrite growth.