Electronic structure and spectroscopic properties of the ground and low-lying excited states of GeSi+ have been studied by using multireference singles and doubles configuration interaction (MRDCI) method that includes relativistic effective core potentials of Ge and Si atoms. At least 17 Lambda-Sigma bound states of GeSi+ are reported within 5 eV. Potential energy curves of 24 Lambda-Sigma states which correlate with the lowest two dissociation limits, Ge+(P-2(u))+Si(P-3(g)) and Ge(P-3(g))+Si+ (P-2(u)) are constructed. The ground-state dissociation energy of GeSi+ is estimated to be 3.116 eV. The spin-orbit coupling among all states correlating the two dissociation limits is also included in the calculations. Spectroscopic constants of 27 Omega states of the ion are reported. Effects of the spin-orbit coupling oil the spectroscopic properties are also studied. Potential energy curves of Omega states show several avoided crossings. Transition probabilities of many electric dipole allowed and spin-forbidden transitions are computed. Transitions such is 2(4)Sigma(-)-X-4 Sigma(-) and 4(4)Sigma(-)-X-4 Sigma(-) are found to be highly probable. Partial lifetimes for some weak spin-forbidden transitions to the ground-state components, X-4 Sigma(-)(1/2) and X-4 Sigma(-)(3/2) are also computed.