  In the framework of the spacetime with torsion, we obtain the flavor
evolution equation of the mass neutrino oscillation in vacuum. A comparison
with the result of general relativity case, it shows that the flavor
evolutionary equations in Riemann spacetime and Weitzenb\"ock spacetimes are
equivalent in the spherical symmetric Schwarzschild spacetime, but turns out to
be different in the case of the axial symmetry.
