Potential energy curves (PECs)for the ground state and several low-lying electronic excited states of BeCl molecule are calculated using the multi-reference configuration interaction (MRCI)method with the basis set of aug-cc-pVTZ where the Davidson correction is considered as an approximation to full CI. The symmetries and dissociation limits for these electronic states are determined through group theory. The PECs of ground state(X2+)and first excited state(A2)are fitted to the Murrell-Sorbie (MS)potential function, and from the fitting parameters the spectroscopic constants are determined to be De=3.74 eV, Re=0.18173 nm(0.17970), we=857.4 cm-1(847.2), wexe=5.03 cm-1(5.14), Be=0.7103 cm-1(0.7285), and e =0.0059 cm-1(0.0069)(where the values in parentheses are the cited experimental results)for X2+ state and De=3.02 eV, Re=0.18369 nm(0.18211), we=832.7 cm-1(822.1), wexe=5.93 cm-1(5.24), Be=0.6953 cm-1(0.7094), and e=0.0065 cm-1(0.0068)for A2 state of BeCl. All the calculation results are in good agreement with the experimental values. In addition, we use the Level program to calculate the radial Schrdinger equation of nuclear motion to obtain the vibrational levels for the X2+ and A2 states.