With the help of the exact diagonalization approach, the Josephson phase transition in a T-shaped double quantum-dot (QD) junction is theoretically investigated. It is found that when the intradot Coulomb interaction in one dot is super-strong, new Josephson phase-transition manner comes into being, in comparison with the case of two identical dots. Besides, owing to the different positions of the two dots, the super-strong Coulomb repulsions in them induce two phase-transition results, respectively. We believe that this work can be helpful in understanding how the super-strong Coulomb interaction influences the phase transition in the Josephson junction with embedded dots.