The millimeter-wave (mm-Wave) or 60 GHz technology emerges as an attractive candidate for indoor wireless access in the 5G architecture. Different from 2.4/5 GHz, high signal attenuation requires mm-Wave antenna utilizing directional transmission to enhance beamforming gain. Consequently, time-consuming beamforming training process between mm-Wave nodes significantly increases communication overhead, especially when the environment is crowded since the nodes perform training process in a contention and backoff manner. In this paper, we propose a novel group beam training scheme that enables simultaneous beam training of all the user devices attempting to associate with the access point. Leveraging the angle-of-arrival sparsity in mm-Wave communications, compressed sensing is adopted to further reduce the beam training overhead. To verify the feasibility of group training and the necessity of compressed sensing under certain conditions, we analyze the signal-to-noise ratio measured on a 60 GHz software defined radio testbed in three typical indoor environments: i) corridor; ii) conference room; and iii) laboratory. Extensive simulations are also performed to evaluate the recovery performance of compressed sensing in mm-Wave WLANs for different sampling capabilities. Simulation results show that compressed sensing reduces the cost of sector sweep by 50%.