The potential energy curves (PECs) of X 1 Σ + ,a ,3 Σ + ,a 3 Π, A 1 Π states for GeO molecule are calculated by the multireference configuration interaction method (MRCI) and MRCI with the Davidson's corrections (MRCI+Q) with aug-cc-pVTZ basis set. All these states involved dissociate into the same dissociation channel Ge( 3 P)+O( 3 P). For the four states, the spectroscopic parameters (R e , D e , ω e , B e , ω e χ e and T e ) have been obtained, which shows that our results are in very good agreement with the experimental value and other theoretical data at MRCI+Q level. The dipole moments of these states are also obtained. In addition, based on the accurate results of spectroscopic constants at MRCI+Q level, the first 30 vibrational states are determined for the four low-lying electronic states when J=0. The vibrational levels G(v) and inertial rotation constants B ν at MRCI+Q level are calculated when J=0, the results of X 1 Σ + and A 1 Π states are in concordance with the available other theoretical values and experimental work. The dissociation limits, dissociation energies, electronic configurations at equilibrium internuclear distance for a ,3 Σ + , a 3 Π states also are predicted for the first time.