  The stellar-mass black hole surrounded by the neutrino-dominated accretion
flow (NDAF) is proposed to be the central engine of the gamma-ray burst (GRB).
In this work, we investigate the neutrino/anti-neutrino luminosity and
annihilation luminosity from the NDAF and pair-annihilation model, taking into
account the neutrino oscillation above the accretion disk. The disk
hydrodynamical properties are modelled using the empirical solution previously
derived with boundary conditions including the effect of electron degeneracy
and neutrino trapping. Our key parameters are the mass accretion rate and the
black hole spin given in the range of $\dot{M} = 0.1$ - $10$ $M_\odot$ s$^{-1}$
and $ 0 \le a < 1$, respectively. Without neutrino oscillation, the obtained
neutrino/anti-neutrino luminosity is $\sim 10^{51}$ - $10^{53}$ $\textrm{erg
s}^{-1}$, while the neutrino annihilation luminosity is found to be $\sim
10^{46}$ - $10^{51}$ $\textrm{erg s}^{-1}$. In the presence of neutrino
oscillation in the vacuum limit, the electron neutrino annihilation luminosity
decreases by $\lesssim 22\%$ through the flavor transformation, while the muon-
and tau-neutrino luminosity can increase up to $\sim 45\%$ and $ 60\%$,
respectively. As a result, the total annihilation luminosity can be reduced up
to $\sim 19\%$ due to the oscillation process above the disk. Finally, we also
investigate the case whereby the CP-violating phase is changed from $\delta
\textrm{CP} =$ $0^{\circ}$ to $245^{\circ}$. However, our results reveal that
the CP-violating phase has minimal impact on neutrino annihilation luminosity.
