We construct a new three-dimensional general relativistic magnetohydrodynamics code, in which a fixed mesh refinement technique is implemented. To ensure the divergence-free condition as well as the magnetic flux conservation, we employ the method by Balsara [J. Comp. Physiol. 174, 614 (2001); J. Comp. Phys. 228, 5040 (2009)]. Using this new code, we evolve differentially rotating magnetized neutron stars, and find that a magnetically driven outflow is launched from the star exhibiting a kink instability. The matter ejection rate and Poynting flux are still consistent with our previous finding [M. Shibata, Y. Suwa, K. Kiuchi, and K. Ioka, Astrophys. J. 734, L36 (2011)] obtained in axisymmetric simulations.