This paper investigates the wireless information surveillance in a suspicious millimeter wave (mmWave) wireless communication system via the spoofing relay based proactive eavesdropping approach. Specifically, the legitimate monitor in the system acts as a relay to simultaneously eavesdrop and send spoofing signals to vary the source transmission rate. To maximize the effective eavesdropping rate, an optimization problem for both hybrid precoding design and power distribution is formulated. Since the problem is fractional and non-convex, we resort to the Dinkelbach method to equivalently reduce the original problem into a series of non-fractional problems, which is still coupling. Afterwards, based on the BCD-type method, the non-fractional problem is reduced to three subproblems with two introduced parameters. Then the GS-PDD-based algorithm is proposed to obtain the optimal solution by alternately optimizing the three subproblems and simultaneously updating the introduced parameters. Numerical results verify the effectiveness and superiority of our proposed scheme.