The Advanced LIGO have detected a number of gravitational-wave events that caused by merging of stellar mass binary black holes (BBHs). We study the dynamical evolution of stellar mass BBHs in a galactic nucleus that contains a massive black hole (MBH). We performed a comprehensive study of BBH merging events in the galactic nucleus, by considering simultaneously the non-resonant and resonant relaxations of the BBHs, the binary-single encounters of the BBHs with the field stars, the Kozai-Lidov (KL) oscillation, and the close encounters between the BBHs and the central MBH. As the BBHs are usually heavier than the background stars, they sink to the center by mass segregation, making the KL oscillation an important
effect in merging BBHs. The binary-single encounters can make BBHs hardening, and thus increase the merging rates significantly. The mergers of BBHs are mainly contributed by galaxies containing MBHs less massive than 10^8 solar masses and the total event rates are likely in orders of 1-10 /Gpc^3/yr,
depending on the detailed assumptions of the nucleus clusters. About 3-10% of these BBH mergers have eccentricities >0.01 when their gravitational wave oscillating frequencies enter the LIGO band (10 Hz). Our results show that merging the BBHs within galactic nuclei can be an important source of the merging events detected by the Advanced LIGO/Virgo, and they can be distinguished from BBH mergers from the
galactic fields and globular clusters when enough events are accumulated.
