Remarkably enhanced photovoltaic effects have been observed in the heterostructures of p-type A-site Nd3+-doped BiFeO3 (Bi0.9375Nd0.0625)FeO3 (or BFONd) polycrystalline ceramics and the n-type ITO thin film. The maximum power conversion is ~0.82%, which is larger than 0.015% in BiFeO3 (BFO) under blue-ultraviolet irradiation of wavelength λ = 405 nm. The current-voltage (I-V) characteristic curve suggests a p-n junction interface between the ITO thin film and BFO (or BFONd) ceramics. The band gaps calculated from first-principles for BFO and BFONd are respectively 2.25 eV and 2.23 eV, which are consistent with the experimental direct band gaps of 2.24 eV and 2.20 eV measured by optical transmission spectra. The reduction of the band gap in BFONd can be explained by the lower electronic Fermi level due to acceptor states revealed by first-principles calculations. The optical calculations show a larger absorption coefficient in BFONd than in BFO.