<p><strong>Abstract.</strong> We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic jet and an unmagnetized sheath plasma. We have examined the strong magnetic fields generated by kinetic shear (Kelvin–Helmholtz) instabilities. Compared to the previous studies using counter-streaming performed by Alves et al. (2012), the structure of the kinetic Kelvin–Helmholtz instability (KKHI) of our jet-sheath configuration is slightly different, even for the global evolution of the strong transverse magnetic field. In our simulations the major components of growing modes are the electric field <i>E</i>_<i>z</i>, perpendicular to the flow boundary, and the magnetic field <i>B</i>_<i>y</i>, transverse to the flow direction. After the <i>B</i>_<i>y</i> component is excited, an induced electric field <i>E</i>_<i>x</i>, parallel to the flow direction, becomes significant. However, other field components remain small. We find that the structure and growth rate of KKHI with mass ratios <i>m</i>_i/<i>m</i>_e = 1836 and <i>m</i>_i/<i>m</i>_e = 20 are similar. In our simulations saturation in the nonlinear stage is not as clear as in counter-streaming cases. The growth rate for a mildly-relativistic jet case (&amp;gamma;_j = 1.5) is larger than for a relativistic jet case (&amp;gamma;_j = 15).</p>