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 ##IMG## [http://ej.iop.org/images/0004-637X/848/2/121/apjaa8e9fieqn1.gif] $500łeqslant ell łeqslant 2100$ , 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 3.1 σ 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 relative to the Planck 2015 best-fit model prediction. We obtain ##IMG## [http://ej.iop.org/images/0004-637X/848/2/121/apjaa8e9fieqn2.gif] $A_L=0.60_-0.24^+0.26(mathrmstat)_-0.04^+0.00(mathrminst)$ ± 0.14(foreground) ± 0.04(multi), where ##IMG## [http://ej.iop.org/images/0004-637X/848/2/121/apjaa8e9fieqn3.gif] $A_L=1$ is the fiducial ΛCDM value.