  With the help of the numerical renormalization group method, we theoretically
investigate the Josephson phase transition in a parallel junction with one
quantum dot embedded in each arm. It is found that in the cases of uniform dot
levels and dot-superconductor couplings, the Josephson phase transition will be
suppressed. This is manifested as the fact that with the enhancement of the
electron correlation, the supercurrent only arrives at its $\pi'$ phase but
cannot enter its $\pi$ phase. Moreover, when the dot levels are detuned, one
$\pi'$-phase island appears in the phase diagram. Such a result is attributed
to the nonlocal motion of the Cooper pair in this structure. We believe that
this work can be helpful in understanding the Josephson phase transition
modified by the electron correlation and quantum interference.
