Laser ranging with frequency comb intermode beats (IMBs) has been suffering from random phase drifts (RPDs) for two decades. In this study, we reveal the influence of signal transmission path on the RPDs and propose a real-time suppression method using two IMBs of similar frequencies from different combs. As the two IMBs obtain similar RPDs during their transmission through same signal paths, the RPD of the original probing signal IMB is suppressed by deducting the RPD of the newly added local IMB in real time. In our experiments, a real-time suppression of RPDs is achieved using IMBs of 1001 and 1000 MHz. For the sampling time of 100 s, the effect of 19-fold suppression has been achieved. The proposed method provides a new solution for the long-standing phase drift problem in laser ranging with comb IMBs.