Electric field-induced antiferroelectric-ferroelectric phase transition and the associated nonlinear dielectric behavior in particulate composites are investigated for achieving a high dielectric capacity. A phenomenological thermodynamic model based on the Landau theory is first developed to discuss the generic phenomena of a temperature-electric field phase diagram, coexistence of antiferroelectric and ferroelectric phases, field-induced antiferroelectric-ferroelectric phase transition, and nonlinear dielectric behavior. The model is then used to carry out the phase field simulation of particulate nonlinear dielectric composites. It is found that the composites exhibit nonlinear dielectric behaviors, and the depolarization field in the composites helps reduce the dielectric hysteresis and enhance the reversibility of antiferroelectric-ferroelectric phase transitions, which are desired for energy storage applications. The simulations also reveal the underlying domain-level mechanisms for nucleation and growth processes of the phase transitions. It is shown that the macroscopic properties of the composites sensitively depend on the directional alignment of the antiferroelectric filler particles, and thus the filler morphology is an effective control variable in designing nonlinear dielectric composites.