Broad band second harmonic generation (SHG) over the spectral range of 530700nm is reported using an epitaxial barium titanate (BaTiO3) thin film waveguide. The epitaxial layers are multidomain consisting of both a and c domain variants. The SHG conversion efficiency is nearly independent of wavelength over the visible spectra range. An enhanced broadband conversion efficiency was observed that is attributed to random quasi-phase matching in the polydomain epitaxial layers. In contrast to theory of SHG for disordered nonlinear media, the observed SHG shows a quadratic dependence on pump power.