We measure cosmic weak lensing shear power spectra with the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalog covering 137 sq. deg. of the sky. Thanks to its depth and excellent-image quality, we obtain a high significance measurement of the cosmic shear power spectra in 4 tomographic redshift bins in the redshift range of 0.3 ≤ z ≤ 1.5, achieving a total S/N of 16 in the multipole range 300 ≤ l ≤ 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. For a flat Λ cold dark matter (ΛCDM) model, we obtain one of tightest constraints on S8 ≡ sigma8 (Omegam /0.3)^alpha = 0.800^{+0.029}_{−0.028} for alpha = 0.45 from our HSC tomographic cosmic shear analysis alone. Although we do not find significant inconsistency with Planck cosmic microwave background constraints, our results prefer slightly lower values of S8 at 2 sigma level as with other lensing surveys such as DES and KiDS and may indicate physics beyond Lambda CDM model. 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 S8 by up to ∼ 0.6σ. The full HSC survey data will contain several times more area, and will lead to significantly improved cosmological constraints.