The unprecedentedly bright optical afterglow of GRB 130606A located by Swift at a redshift close to the reionization era ( z = 5.913 ) provides a new opportunity to probe the ionization status of intergalactic medium ( IGM ) . Here we present an analysis of the red Ly \alpha damping wing of the afterglow spectrum taken by Subaru/FOCAS during 10.4–13.2 hr after the burst . We find that the minimal model including only the baseline power-law and H \emissiontype I absorption in the host galaxy does not give a good fit , leaving residuals showing concave curvature in 8400–8900 Å with an amplitude of about 0.6 % of the flux . Such a curvature in the short wavelength range can not be explained either by extinction at the host with standard extinction curves , intrinsic curvature of afterglow spectra , or by the known systematic uncertainties in the observed spectrum . The red damping wing by intervening H \emissiontype I gas outside the host can reduce the residual by about 3 \sigma statistical significance . We find that a damped Ly \alpha system is not favored as the origin of this intervening H \emissiontype I absorption , from the observed Ly \beta and metal absorption features . Therefore absorption by diffuse IGM remains as a plausible explanation . A fit by a simple uniform IGM model requires H \emissiontype I neutral fraction of f _ { H \emissiontype { I } } \sim 0.1–0.5 depending on the distance to the GRB host , implying high f _ { H \emissiontype { I } } IGM associated with the observed dark Gunn-Peterson ( GP ) troughs . This gives a new evidence that the reionization is not yet complete at z \sim 6 .