Charge-transfercross sections of the ground state He⁺ ions in collisions with He atoms and simple molecules (H₂, D₂, N₂, CO and CO₂) have been measured in the energy range of 0.20 to 4.0 keV with the initial growth rate method. Since previously published experimental data are scattered in the low energy region, the present observations would provide reasonably reliable cross section data below 4 keV. The charge transfer accompanied by dissociation of product molecular ion can be dominant at low energies for molecular targets. In He⁺ + D₂ collisions, any isotope effect was not observed over the present energy range, compared to H₂ molecule.