The gyrokinetic-Vlasov simulation code (GKV code) is applied to zonal flows and the ion temperature gradient (ITG) turbulence in helical systems with L = 2 and M = 10 like the Large Helical Device (where L and M denote poloidal and toroidal periodicities of the main helical component of the confinement field, respectively) for the standard and inward-shifted model configurations. Because of the slower radial drift motion of helical-ripple-trapped particles, the inward-shifted case provides a higher zonal-flow response than that in the standard model with smaller side-band helical field components. The nonlinear GKV simulations show that the ITG turbulent transport in the inward-shifted model, which has larger growth rates of the ITG stability, is regulated by the zonal flows to a level comparable to the standard case.