Cross sections for transitions among the Na(3p2Pjm) states induced by He(1S) collisions are calculated for impact energies E<or=0.07 eV by a close coupled wave treatment with an orientation-dependent interaction. The cross section sigma (j'm';jm) for the transition in which the total angular momentum j and its projection m are changed to j' and m', the cross section sigma (j';j) for j to j' transition in which an average over m and a summation over m' are taken, the angular distribution d sigma (j'j mod theta )/d theta , the multipole relaxation cross sections and the polarization transfer cross section sigma pt are evaluated.