The potential energy curves of 18 Λ-S states of the P2 + cation have been constructed using the internally contracted multi-reference configuration interaction approach combined with the Davidson correction. The basis-set extrapolation to the complete basis set limit is performed. The relativistic effect is considered in calculations. Treatment of scalar relativistic effect at the third-order Dkroll-Hess approximate and spin-orbit coupling with the state-average Breit-Pauli operator is made. Based on the obtained potential energy curves, the spectroscopic parameters for all bound Λ-S and Ω states are determined. These results are in agreement with experiment where the spectroscopic data are available. The transition dipole moments are calculated. The properties of the dipole-allowed transitions among doublet or quartet Λ-S states are evaluated, from which Einstein coefficients, Franck-Condon factors and radiative lifetimes are estimated. The spin-orbit coupling effect on the transition properties of the 12Πg→X2Πu system is also studied. The spectroscopic and transition properties reported in this study can be used to guide the detection of phosphorus dimer cation in spectroscopy experiments.