We present He i/Hβ flux and He/H abundance ratios in three James Webb Space Telescope galaxies with significant constraints on N/O abundance ratios, GS-NDG-9422, RXCJ2248-ID, and GLASS150008 at z ∼ 6 mostly with the spectroscopic coverage from He i λ4471 and He ii λ4686 to He i λ7065, and comparing with 68 local dwarf galaxies. We find that these high-z galaxies present strong He i emission with He i/Hβ flux ratios generally larger than those of local dwarf galaxies. We derive He/H with all of the detected Hei, He ii, and 2−3 hydrogen Balmer lines in the same manner as the local He/H determination conducted for cosmology studies. These high-z galaxies show He overabundance He/H ≳0.10 or high electron density of n e ∼ 103−4 cm−3 much larger than local values at low O/H, 12+log(O/H)=7−8 . In contrast, we obtain low He/H and n e values for our local dwarf galaxies by the same technique with the same helium and hydrogen lines, and confirm that the difference between the high-z and local dwarf galaxies is not mimicked by systematics. While two scenarios of (1) He overabundance and (2) high electron density are not clearly concluded, we find that there is a positive correlation between the He/H–N/O or n e–N/O plane by the comparison of the high-z and local dwarf galaxies. Scenario (1) suggests that the overabundant helium and nitrogen are not explained by the standard chemical enrichment of core-collapse supernovae, but by the CNO-cycle products and equilibrium ratios, respectively. Scenario (2) indicates that the strong helium lines originated from the central dense clouds of the high-z galaxies by excessive collisional excitation.