In future 5G communication systems, the mm-wave transmission is considered as a key solution to fulfill the growing demands in mobile traffic. To overcome the high propagation loss experienced at high frequencies, mm-wave transmission relies heavily on highly directional antennas. Because directional transmission is sensitive to position changes, the existing handover strategies which only consider the instantaneous received signal strength fails to provide robust connections for moving users. In this paper, we propose an improved handover strategy for mm-wave mobile networks taking the connection robustness issue into account. The connection robustness is evaluated in terms of the effective beam coverage probability, which is defined as the probability that a user stays in the coverage area of the same beam after a certain time interval. We show that the proposed handover strategy can reduce handover frequency up to 35% with negligible throughput loss compared to the existing signal strength based scheme.