POLAR is a dedicated Compton scattering polarimeter to detect Gamma-Ray Bursts (GRBs) in the energy range of about 50 to 500 keV, which was launched on-board the Chinese space laboratory Tiangong-2 (TG2) on Sep 15, 2016. Since then, POLAR has detected 55 GRBs jointly with other telescopes as of Apr 1, 2017. Meanwhile, more GRBs detected by POLAR only will be revealed as the burst search and identification program gets more sophisticated to deal with the complicated background. After subtracting the non-observation period due to varies reasons in the commissioning phase, the effective observation time is about 3180 hours, thus the GRB detection rate of POLAR is estimated to be about 150 GRBs/year, demonstrating that POLAR is one of the most sensitive GRB detectors in operation. Thanks to the high sensitivity, large FOV (about 1/2 of the all-sky) and unique capability of polarization measurement, POLAR is a very important detector in the search for high-energy electromagnetic counterpart for Gravitational Wave Bursts (GWB), High Energy Neutrinos (HEN) and Fast Radio Bursts (FRB). In this paper, we summarized the GRB observation by POLAR, including GRB search and identification, joint observation and Gamma-ray Coordinates Network (GCN) alerts, data analysis, GRB catalogues and so on.