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We have investigated the influence of jet rotation and differential motion on the linear and nonlinear development of the current-driven (CD) kink instability of force-free helical magnetic equilibria via threedimensional relativistic magnetohydrodynamic simulations. In this study, we follow the temporal development within a periodic computational box. Displacement of the initial helical magnetic field leads to the growth of the CD kink instability. In rotating relativistic jet case, developed helical kink structure propagates along jet axis with continuous growth of kink amplitude. The growth rate of CD kink instability does not depend on the jet rotation. The coupling of multiple unstable wavelengths is crucial to determining whether the jet is eventually disrupted in nonlinear stage. The strongly deformed magnetic field via CD kink instability may trigger of magnetic reconnection in the jet

Current-Driven Kink Instability in Magnetically Dominated Rotating Relativistic Jet