MmWave in the unlicensed 60GHz band is highly discussed due to the rapid growth of wireless communication services. The utilization of microwave spectrum below 10 GHz is almost reaching its limit. Beamforming (BF) has become an essential technique to compensate the high path loss phenomenon of mmWave. IEEE 802.11ad and 802.11ay standardization task group institute directional multi-gigabit (DMG) wireless local area networks (WLANs) supporting mmWave techniques. With wireless devices explosively increasing, the limited number of BF slots in conventional DMG protocols leads to high packet collision probability, which potentially degrades the system performance. Most of the existing research does not take the multi-user BF contention problem into consideration. In this paper, we design a non-slotted association beamforming training (A-BFT) frame structure for multi-users without separating A-BFT slots in order to alleviate packet collisions due to the shortage of contention and training frames. This new proposed structure allows collisions with useful information left in remaining non-collided slots or frames in order to leverage the insufficiency of BF training for multiple devices. Furthermore, in order to further reduce BF collision probability, we propose two multiuser beamforming training mechanisms, including the time-based distributed coordination function (TDCF) and time-based beam-collision avoidance (TBCA) schemes. Simulation results demonstrate that our new proposed frame structure along with proposed TDCF and TBCA mechanisms outperforms 802.11ad protocol.