Recently,there have been great interest and advancement in the field of laser cooling and magneto-optical trapping of molecules.The rich inteal structure of molecules naturally lends themselves to extensive and exciting applications.In this paper,the radical 138Ba19F,as a promising candidate for laser cooling and magneto-optical trapping,is discussed in detail.The highly diagonal Franck-Condon factors between the X2Σ11/2 and A2Π1/2 states are first confirmed with three different methods.Afterwards,with the effective Hamiltonian approach and irreducible tensor theory,the hyperfine structure of the X2Σ+1/2 state is calculated accurately.A scheme for laser cooling is given clearly.Besides,the Zeeman effects of the upper (A2Π1/2) and lower (X2Σ+1/2) levels are also studied,and their respective g factors are obtained under a weak magnetic field.Its large g factor of the upper state A2Π1/2 is advantageous for magneto-optical trapping.Finally,by studying Stark effect of BaF in the X2Σ+1/2,we investigate the dependence of the inteal effective electric field on the applied electric field.It is suggested that such a laser-cooled BaF is also a promising candidate for precision measurement of electron electric dipole moment.