Chaotic laser characteristics of an optoelectronic oscillator are investigated theoretically and numerically, and the influences of the offset phase and the feedback strength on the time-delay signature of chaos which is generated by an optoelectronic oscillator are studied, based on the method of autocorrelation function. Numerical analyses show that the increase of the feedback strength can further suppress or even conceal the time-delay signature. The closer to the extreme point of the transmission curve the operating point corresponding to the DC offset phase, the weaker the time-delay signature is. The time-delay signature can be suppressed obviously as the offset phase is set to be 0. We also find that the sign of the correlation coefficient corresponding to the time-delay signature is changed when the offset phase and the phase shift caused by the delay feedback produce a phase-shift value of π/2.