The demand of high data rate requirement and spectrum scarcity in the current wireless communication drives the next generation communication technology to mm-wave frequencies. Researches in directivity improvement and multi-functionality of antenna are the determinant factor to provide high data rate and quality of services. This research discourses directivity optimization of a single microstrip rectangular patch antenna with dualband service for mm-wave mobile communication using binary-coded genetic algorithm. Optimization has been done by dividing the patch geometry into 100 small circular cells and assigning them as conducting and none conducting. The proposed antenna was iteratively simulated using a combination of HFSS and MATLAB, and obtained S11 < –10 dB bandwidth (BW) of 2.9% at 28.0 GHz with peak directivity 8.6dB and BW of 1% at 31.1 GHz with peak directivity 10.9dB.