Using the density functional B3P86/cc-PV5Z method, the geometric structure of AlH molecule under different external electric fields are optimized, and the bond lengths, dipole moments, vibration frequencies and other physical properties parameters are obtained. The potential energy curves under different external fields are also obtained by CCSD(T) method with the same basis set. These results show that the properties parameters and potential energy curves may change with different external electric field, especially in the reverse electric fields. The potential energy function without external electric field is fitted by Morse potential, and the potential energy curves under different external fields are fitted using constructed potential model, which adopted the dipole approximation theory. It is found that the fitting parameters are good agreement with experimental values and the critical dissociation electric parameter is consistent with numerical calculation. These results will provide important theoretical and experimental reference for further studying the molecular spectrum, dynamics and molecular cooling with Stark effect.