Based on the physical energy expression of diatomic molecule, an analytical formula is developed by taking multiple differences to predict the R-branch rovibrational transition spectral lines of diatomic system. Only 15 accurate experimental transition lines, and two rotational constants Bv, Bv corresponding to transition band (v, v) are needed when the new formula is used. The new formula is used to study the transition lines of (3, 7) and (4, 8) bands of the A2uX2g system of Cl2+ ion. Not only the experimental transition lines are reproduced, but also the lost ones, especially the high-lying transitions ones are obtained.