The potential energy curves (PECs) of BO molecule, including \sum and \prod symmetries with doublet spin multiplicities, are obtained employing multi-reference configuration interaction (MRCI) method and Dunning’s correlation consistent basis sets. The analytical potential energy functions (APEFs) are fitted using the Murrell-Sorbie (MS) function and the least square method. Based on the PECs, the spectroscopic constants of the states have been determined and compared with the theoretical and experimental results available to affirm the accuracy and liability of the calculations. The root-mean-square (RMS) errors between the fitted results and the ab initio values are too little in comparison with the chemical accuracy (349.755 cm-1. It is shown that the present APEFs are accurate and can display the interaction between the atoms well. The present APEFs can be used to construct more complicated APEF or do some dynamic investigations.