We investigate the possibility of the r-process during the magnetohydrodynamical (MHD) explosion of supernova in a massive star of 13M ⊙ with the effects of neutrinos included. Contrary to the case of the spherical explosion, jet-like explosion due to the combined effects of rotation and magnetic field lowers the electron fraction significantly inside the layers. We find that the ejected material of low electron fraction responsible for the r-process comes out from the inner deep region of the core that is made up of iron-group nuclei. This leads to the production of the second to third peak in the solar r-process elements. We suggest that there are some variations in the r-process nucleosynthesis according to the initial conditions of rotational and magnetic fields.