Pulsed power equipment is often characterized by high energy density and field intensity. In the presence of strong electric field intensity, charge accumulation within insulators exacerbates electric field non-uniformity, leading to potential insulation breakdown, thereby posing a significant threat to the safe operation of pulsed power equipment. In this manuscript, we introduce nonlinear composite materials with field-dependent conductivity and permittivity to adaptively regulate the distribution of the pulsed electric field in insulation equipment. Finite-element modeling and analysis of the needle-plate electrodes and high-voltage bushing are carried out to comprehensively investigate the non-uniformity of the distribution of the electric field and the homogenization effect of various nonlinear materials in the presence of pulsed excitations of different timescales. Numerical results indicate that the involvement of nonlinear composite materials significantly improves the electric field distribution under pulse excitations. In addition, variations in the rising time of the pulses affect the maximum electric field intensity within the insulators considerably, but for pulses of nanosecond and microsecond scales, the tendencies are the opposite. Finally, via the simulations of the bushing, we illustrate that some measures proposed for improving the uniformity of the electric field under low frequencies, e.g., increasing the length of the electric field equalization layer and the distance of the underside of the electric field equalization layer from the grounding screen, are still effective for the homogenization of pulsed electric field.