  We investigate the possibility of explaining the propagation of neutrinos
measured by the OPERA experiment with $\delta v_\nu=(v_\nu-c_0)/c_0$, where
$c_0$ is the speed of light in vacuum, using a bimetric relativity model. The
geometry of the bimetric model has two metrics in spacetime. One metric
$g_{\mu\nu}$ possesses a null cone along which massless gravitons and photons
travel with the constant speed $c_0$, while the other `matter' metric ${\hat
g}_{\mu\nu}=g_{\mu\nu}+\beta\psi_\mu\psi_\nu$ has a null cone with a bigger
speed $c > c_0$ with $0 < \delta v_\nu\ll c/c_0$. This second cone structure of
spacetime prevents the neutrinos from being superluminal tachyons $v_\nu < c$.
Such superluminal neutrinos would lead to severe depletion of neutrino energy,
refuting the OPERA result. The charge-current source of the background gauge
field $\psi_\mu$ is assumed to be baryon charge and the strength of the field
$\psi_\mu$ is distance dependent, explaining the observation that for supernova
SN1987a $v_\nu\simeq c_0$. Altering the path of the neutrinos through the earth
or performing a space experiment can test the OPERA neutrino experimental
result.
