The parity-nonconserving asymmetry in the deuteron photodisintegration, $\vec{\gamma}+d\to n+p$, is considered with the photon energy ranged up to 10 MeV above the threshold. The aim is to improve upon a schematic estimate assuming the absence of tensor as well as spin-orbit forces in the nucleon-nucleon interaction. The major contributions are due to the vector-meson exchanges, and the strong suppression of the pion-exchange contribution is confirmed. A simple argument, going beyond the observation of an algebraic cancellation, is presented. Contributions of meson-exchange currents are also considered, but found to be less significant.