This work mainly studies physical properties of bi-exciton in a finite length conjugated polymer under applied electrical field using long-range electronic correlation model. It is found that long-range correlation effect increases binding energy of bi-exciton, localization of bi-exciton and reverse polarization, so that the long-range correlation effect increases stable ability of double exciton. Under a given applied electrical field, it is found that the reverse polarization and charge transfer quantities increase with increasing electron-electron interaction V under a given Hubbard interaction U, and dipole moment decreases linearly with increasing V. Linear polarizability first increase and then decrease and reaches its maximum value at $V=0.0950$ eV. It is also found that, as the applied electrical field increase, both electron-electron interaction and the long-range correlation effect enhance the linear polarizability and dipole moment before the double exciton is dissolved; when the bi-exciton is dissolved into a positive polaron and a negative polaron, the electron-electron interaction and the long-range correlation effect lowers the linear polarizability but enhance the dipole moment.