We report an improved measurement of the cosmic microwave background B-mode polarization power spectrum with the Polarbear experiment at 150 GHz. By adding new data collected during the second season of observations (2013-2014) to re-analyzed data from the first season (2012-2013), we have reduced twofold the band-power uncertainties. The band powers are reported over angular multipoles 500 â ¤ â â ¤ 2100, where the dominant B-mode signal is expected to be due to the gravitational lensing of E-modes. We reject the null hypothesis of no B-mode polarization at a confidence of 3.1Ï including both statistical and systematic uncertainties. We test the consistency of the measured B-modes with the Î Cold Dark Matter (Î CDM) framework by fitting for a single lensing amplitude parameter AL= 0.60 +0.26-0.24(stat)+0.00-0.04(inst) ± 0.14(foreground) ± 0.04(multi), where AL= 1 relative to the Planck 2015 best-fit model prediction. We obtain ±0.14(foreground) ±0.04(multi), where is the fiducial Î CDM value.