We measure cosmic weak lensing shear power spectra with the Subaru Hyper Suprime-Cam ( HSC ) survey first-year shear catalog covering 137 deg ^ { 2 } of the sky . Thanks to the high effective galaxy number density of \sim 17 arcmin ^ { -2 } even after conservative cuts such as magnitude cut of i < 24.5 and photometric redshift cut of 0.3 \leq z \leq 1.5 , we obtain a high significance measurement of the cosmic shear power spectra in 4 tomographic redshift bins , achieving a total signal-to-noise ratio of 16 in the multipole range 300 \leq \ell \leq 1900 . We carefully account for various uncertainties in our analysis including the intrinsic alignment of galaxies , scatters and biases in photometric redshifts , residual uncertainties in the shear measurement , and modeling of the matter power spectrum . The accuracy of our power spectrum measurement method as well as our analytic model of the covariance matrix are tested against realistic mock shear catalogs . For a flat \Lambda cold dark matter ( \Lambda CDM ) model , we find S _ { 8 } \equiv \sigma _ { 8 } ( \Omega _ { m } / 0.3 ) ^ { \alpha } = 0.800 ^ { +0.029 } _ { -0.028 } for \alpha = 0.45 ( S _ { 8 } = 0.780 ^ { +0.030 } _ { -0.033 } for \alpha = 0.5 ) from our HSC tomographic cosmic shear analysis alone . In comparison with Planck cosmic microwave background constraints , our results prefer slightly lower values of S _ { 8 } , although metrics such as the Bayesian evidence ratio test do not show significant evidence for discordance between these results . We study the effect of possible additional systematic errors that are unaccounted in our fiducial cosmic shear analysis , and find that they can shift the best-fit values of S _ { 8 } by up to \sim 0.6 \sigma in both directions . The full HSC survey data will contain several times more area , and will lead to significantly improved cosmological constraints .