An optoelectronic oscillator with time delay varying feedback is an important means for generating laser chaos signals in a high speed optical chaos security communication system. Three typical routes to laser chaos (cataclysm, periodic and quasi periodic oscillations, and ‘breather’ oscillations) and their characteristics are investigated in detail through analyzing the Hopf bifurcation behaviors. The simulation shows that with the increase of time delay, the complex degree of the output signal increases, and when the time delay is large enough, there occur periodic pulse phenomena within a limited time range. In addition, there exists a critical point caused possibly by the filer, at which the phase diagram changes suddenly, but the complex degree of the output signal does not change obviously.