The gigahertz unlicensed bandwidth spectrum endows millimeter-wave (mmWave) communications with the great potential of realizing high data transmission rates. Similar to all wireless transmission technologies, mmWave communications are also susceptible to security threats. This problem becomes more serious for cooperative networks that need more information exchanges. In this paper, we investigate the secrecy beam-forming designs for mmWave two-way amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relaying networks. To control hardware size and cost, an additional rank constraint is posed on the forwarding matrix at the relay to control the number of analog-to-digital converters (ADCs). In general, the considered optimization problem is nonconvex and very challenging. Based on iterative optimization algorithms, the secrecy beamforming designs are successfully decoupled into a series of convex subproblems that can be solved efficiently. Finally, numerical experiments are conducted to demonstrate the performance advantages of the proposed secrecy beamforming designs.