Self-oscillations of non-neutral plasma diode operating in the anode-glow mode are analysed using the self-consistent one-dimensional Particle-in-Cell Monte Carlo collisions model. In order to obtain these states, the current exceeding the space-charge limited current has to be emitted from the cathode, the electron mean free path must be much longer than the cathode-anode gap, and the cathode voltage must be slightly larger than the ionization potential of the background gas. It is obtained that in such a case, immobile ions form the electrostatic trap for the electrons generated in the cathode-anode gap. These electrons oscillate between the cathode and the anode causing the self-oscillations of the plasma potential. It is shown that the increase of the emission current leads to the increase of the frequency of the obtained self-oscillations. Starting at some value of the emission current, a lot of the emitted electrons are got trapped in the electrostatic well, which leads to the transition to chaos.