To investigate the correlation between the activation energy E ac and electronic structure near the band gap for impurity-type H + -ion conductors, we measured infrared reflectivity spectra of sintered BaCe 1-x M x O 3 (x=0, 0.10, 0.15 for M=Nd and x=0.05, 0.1 for M= Gd) at room temperature, and estimated optical dielectric constant and the phonon frequencies of LO-and TO-modes with Kramers-Kronig analysis. We found a clear proportionality represented as E ac -0.14=[1/( -1.4)]. The proportional form is shifted from that of superionic conductor. For the origin of the shift, we attribute weakened influence of the Coulomb force of the host lattice on mobile H + -ion. This mechanism is confirmed from the volume and mass dependences of E ac values, and also from reasonable interpretation about smaller E ac value of AB 1-x M x O 3 than that of ABO 3 with respect to the impurity electronic levels near the band edge.