In this paper, the QCISD(T), CCSD(T), B3PW91 and B3LYP methods and the basis sets of aug-cc-pVTZ, 6-311G are used to calculate the structure of the ground state of free radical BeH molecule. The equilibrium distance and the energy of the molecule are optimized. The calculated results are compared with the experimental data, and the B3LYP method with the basis sets 6-311G is found to be able to provide the results that are the closest to the experimental values. So, in this paper the density function B3LYP method and the basis sets 6-311G are chosen and used to optimize the geometric structures of the ground state of free radical molecule of BeH in electric fields ranging from -0:02 to 0:02 a.u. The effects of external electric field on bond distance, system energy, charge distribution, energy levels, dipole moment, HOMO-LUMO gap, and infrared spectrum are studied．The results show that the molecular bond distance, the total atomic charge, the dipole moment, and the IR intensity decrease gradually with the increase of the external electric field along the molecular axis H→Be. At the same time, the total energy, the HOMO-LUMO gap, and the frequencies increase. The total energy increases sharply while the reverse electric field Be→H increases.