Millimeter Wave (mmWave) communication is considered as an enabling technology for the next generation of cellular networks because it offers much larger bandwidth and higher data rate than the current lower-frequency cellular systems to satisfy the exponential growth of mobile data demand. High gain directional antennas are needed to overcome high propagation losses in mmWave bands. However, the reliance on highly directional antennas will result in a more complicated initial cell search procedure since both base station and mobile device have to look for each other over a large space to establish the link. This paper focuses on analyzing the performance of the directional cell search procedure where the base stations periodically transmit signals in a set of optimal directional patterns to scan the coverage area. The mobile terminals detect the signals from the base station using the Generalized Likelihood Ratio Test (GLRT). The results show that with an appropriate scanning scheme, the use of directional antennas can outperform their omnidirectional counterparts in terms of signal detection performance as well as total time required.