The X1Σ+, a3Π and A1Π states of BCl molecule are studied using the highly accurate valence internally contracted multireference configuration interaction approach including the Davidson modification. The Dunning's correlation-consistent basis sets, aug-cc-pV6Z and aug-cc-pV5Z, are used in the study. To obtain more reliable results, the potential energy curves (PECs) of three electronic states are extrapolated to the complete basis set limit by the two-point total-energy extrapolation scheme. The effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. By fitting these PECs, the spectroscopic parameters (Te, Re, ωe, ωexe, Be, αe and De) of the X1Σ+, a3Π and A1Π states of BCl are determined. These parameter values coincide with the experimental results. In addition, the whole vibrational states for X1Σ+, a3Π and A1Π states at J =0 (J is the rotational quantum number) are determined by numerically solving the radical Schrödinger equation of the nuclear motion of diatomic molecules. For each vibrational state, the vibrational level and inertial rotation constants are obtained, which are in excellent accordance with the experimental results. With the potential energy curves obtained at MRCI+Q/56+CV+DK level and the MRCI wave functions, the Franck-Condon factors, radiative lifetime of transition from a3Π and A1Π to the ground state are computed.