Full-wave analysis has been applied to the study of wave propagation in a nonuniform plasma, especially where WKB approximation becomes invalid. Because of several approximations assumed, however, it cannot be applied to problems involving particle kinetic effects or nonlinear processes. To evaluate such complicated effects on wave propagation in a nonuniform plasma, we have performed particle simulations with a one-dimensional nonuniform electron plasma, in which a wave propagates parallel to the static magnetic field. Good agreement is found between the wave fields in the particle simulations and the full-wave solutions under the same plasma conditions. We also found that two interesting phenomena occur in the particle simulations with plasma conditions different from those allowed in full-wave analysis. One is a particle kinetic effect, which is due to a large thermal velocity of the plasma. A whistler mode wave is spatially attenuated in a nonuniform plasma through cyclotron damping. The other is a nonlinear effect arising when the incident wave has a large amplitude. Several electromagnetic modes propagating in a nonuniform plasma interact nonlinearly with one another to excite electrostatic oscillations at the local plasma frequencies and at twice the wave frequency. Particle simulation and full-wave analysis can be used together to characterize wave propagation under a fuller range of plasma conditions and to clarify the limitation of each.