Nonlinear dynamical behaviors of plasma in the Pierce diode are investigated by a numerical code developed using a one dimensional fluid model. The plasma in Pierce diode is alternately stable and unstable as Pierce parameter is changed. The dynamical characteristics of neutral and non-neutral Pierce system is examined analytically and numerically. It alternately has growing and oscillatory mode as Pierce parameter varies. As Pierce parameter is decreased, each oscillatory mode undergoes a sequence of subharmonic period-doubling bifurcation and then culminate in a chaotic strange attractor. The analysis for this nonlinear behavior can be used as a model for understanding of beam-plasma interaction in more complex geometries and a data for chaos control.