The potential energy curves （PECs） for the ground state （X1Σ+） and six excited states （a3П, A1П, B1Σ+, b3Σ-,c3Σ+, and C′1Δ） of BH molecule have been computed using the multireference configuration interaction （MRCI） method and Dunning’s correlation consistent basis sets aug-cc-pV5Z. By employing the Murrell-Sorbie function （MS） and the least-square fitting method, the analytical potential energy functions （APEFs） of these states are obtained. The root means square （RMS） errors between the fitted results and the ab initio values are very small in comparison with the chemical accuracy （349755 cm-1）, which implies that the APEFs can well display the interactions between the two atoms of BH molecule. Based on the APEFs, we have calculated the spectroscopic parameters and compared them with the available theoretical and experimental values. The calculating results are in good agreement with the experimental values, which shows that the present APEFs are accurate. The double-well PEC for the B1Σ+ state has also been fitted accurately with MS function, which provides a sample for more wider application of MS function.