Gyrokinetic theory and simulation results are presented to investigate regulation of ion temperature gradient (ITG) turbulence due to E × B zonal flows in helical systems. In order to examine effects of changes in helical magnetic configuration on anomalous transport and zonal flows, magnetic field parameters representing the standard and inward-shifted configurations of the Large Helical Device (LHD) [O. Motojima, N. Ohyabu, A. Komori, et al., Nucl. Fusion 43, 1674 (2003)] are used. The linear gyrokinetic analyses show that the largest growth rate of the linear ITG instability for the inward-shifted configuration is slightly higher than that in the standard one while, as theoretically predicted, zonal flows generated by given sources keep larger values for longer time for the inward-shifted case because of a smaller safety factor, a lower aspect ratio, and slower radial drift velocities of helical-ripple-trapped particles. It is shown from the gyrokinetic Vlasov simulation of the ITG turbulence that, in spite of the higher ITG-mode growth rate, the inward-shifted plasma takes a smaller average value of the ion thermal diffusivity in the steady turbulent state with a higher zonal-flow level. These results imply that neoclassical optimization contributes to reduction of the anomalous transport by enhancing the zonal-flow level and give a physical explanation for the confinement improvement observed in the LHD experiments with the inward plasma shift. When equilibrium radial electric fields produce poloidal E × B rotation of helically-trapped particles with reduced radial displacements, further enhancement of zonal flows and resultant transport reduction are theoretically expected.