The potential energy curves (PECs) of X-2 Sigma(+), A(2)Pi r and B-2 Sigma(+) states of BeF radical have been investigated using the complete active space self-consistent-field (CASSCF) method, followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach at the correlation-consistent basis sets, cc-pV5Z for Be and aug-cc-pV6Z for F. Based on the PECs of X-2 Sigma(+), A(2)Pi r and B-2 Sigma(+) states, the spectroscopic parameters (D-e, R-e,omega(e),omega(e)chi(e), a(e) and B-e) have also been determined in the present work. With the PECs determined at the present level of theory, vibrational states have been predicted for each state when the rotational quantum number J equals zero (J = 0). The vibrational levels, inertial rotation and centrifugal distortion constants are determined for the three states, and the classical turning points are also calculated for the X-2 Sigma(+) state. Compared with the available experiments and other theories, it can be seen that the present spectroscopic parameter and molecular constant results are more fully in agreement with the experimental findings.