WWe have investigated 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 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 E _ { z } and the magnetic field B _ { y } . After the B _ { y } component is excited , an induced electric field E _ { x } becomes significant . However , other field components remain small . We find that the structure and growth rate of KKHI with mass ratios m _ { i } / m _ { e } = 1836 and m _ { i } / m _ { 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 ( \gamma _ { j } = 1.5 ) is larger than for a relativistic jet case ( \gamma _ { j } = 15 ) .