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 ≤ ℓ ≤ 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 3.1σ including both statistical and systematic uncertainties. We test the consistency of the measured B-modes with the Λ Cold Dark Matter (ΛCDM) framework by fitting for a single lensing amplitude parameter A L = 0.60 +0.26-0.24(stat)+0.00-0.04 (inst) ± 0.14(foreground) ± 0.04(multi), where A L = 1 relative to the Planck 2015 best-fit model prediction. We obtain ±0.14(foreground) ±0.04(multi), where is the fiducial ΛCDM value.