The composition of positive ions, H+, H2+, and H3+, in high-density H2 plasmas was measured using a time-of-flight mass spectrometer which was attached behind the end plate of a linear helicon-wave plasma source. The dominant ion was H3+ when electron density was below 3.5×1011 cm-3, while in high-density plasmas with ne≥8×1011 cm-3, H+ and H2+ were dominant at similar fractional abundances. In the afterglow plasma, the fractional abundance of H2+ decreased rapidly with a time constant of ∼3 µs. Simultaneously with the disappearance of H2+, H3+ became dominant in the late afterglow. The above experimental results were examined by a rate equation analysis based on available reaction rate coefficients. The results of the rate equation analysis were qualitatively consistent with the experimental observations.