The hybrid density functional theory is used to study formation of the junction of alkanemonothiol molecules with different terminal groups. The relationship between geometric structures of the molecular junction and the external force is obtained. On the basis of the relationship, the electronic transport properties of the molecular junctions under different external forces are investigated using the elastic-scattering Green’s function method. The results show that the C11S molecular junction is broken when the distance of the two electrodes is larger than 2.1 nm. While for C11SOH and C10SCOOH molecular junctions, their critical distances are similarly 2.15 nm. Taking the same external force, we find that the C11S molecule has the largest conducting ability, and the C10SCOOH molecule has the smallest conducting ability. Furthermore, the conductance of the three molecular junctions is monotonically enhanced with the increase of the external force. The numerical results are consistent with the experimental findings qualitatively.