By the close-coupling calculation the cross sections are evaluated for rotational transitions by low energy (0.01∼10 eV) electron impact in two polar molecules, CN and HCl. The transitions from the ground state of rotation are considered and the cross sections σ( l =→ l =0), σ(0→1), σ(0→2) are calculated, l representing the rotational state of the molecule. For σ(0→1), comparison with the calculation in the Born approximation is made and it is shown that the Born results are fairly accurate even for a quite large dipole moment (at least up to 1 e a 0 , a 0 being the Bohr radius). There occurs a shape resonance in the elastic process 0→0, which may explain the peak appearing at about 10 eV of the incident energy in the measured total cross section for e -HCl collision. Finally the dependence of the calculated cross sections on the dipole moment is discussed.