  We study theoretically the Josephson effect between two time-reversal
two-band superconductors, where we assume the equal-time spin-singlet $s$-wave
pair potential in each conduction band. %as well as the band asymmetry and the
band hybridization in the normal state. The superconducting phase at the first
band $\varphi_1$ and that at the second band $\varphi_2$ characterize a
two-band superconducting state. We consider a Josephson junction where an
insulating barrier separates two such two-band superconductors. By applying the
tunnel Hamiltonian description, the Josephson current is calculated in terms of
the anomalous Green's function on either side of the junction. We find that the
Josephson current consists of three components which depend on three types of
phase differences across the junction: the phase difference at the first band
$\delta\varphi_1$, the phase difference at the second band $\delta\varphi_2$,
and the difference at the center-of-mass phase $\delta(\varphi_1+\varphi_2)/2$.
A Cooper pairs generated by the band hybridization carries the last current
component. In some cases, the current-phase relationship deviates from the
sinusoidal function as a result of time-reversal symmetry breaking down.
