We compare the CO (J = 1-0) and H I emission in the Large Magellanic Cloud in three dimensions, i.e., including a velocity axis in addition to the two spatial axes, with the aim of elucidating the physical connection between giant molecular clouds (GMCs) and their surrounding H I gas. The CO J = 1-0 data set is from the second NANTEN CO survey and the H I data set is from the merged Australia Telescope Compact Array (ATCA) and Parkes Telescope surveys. The major findings of our analysis are as follows: (1) GMCs are associated with an envelope of H I emission, (2) in GMCs [average CO intensity] [average H I intensity]1.1±0.1, and (3) the H I intensity tends to increase with the star formation activity within GMCs, from Type I to Type III. An analysis of the H I envelopes associated with GMCs shows that their average line width is 14 km s–1 and the mean density in the envelope is 10 cm–3. We argue that the H I envelopes are gravitationally bound by GMCs. These findings are consistent with a continual increase in the mass of GMCs via H I accretion at an accretion rate of 0.05 M yr–1 over a timescale of 10 Myr. The growth of GMCs is terminated via dissipative ionization and/or stellar-wind disruption in the final stage of GMC evolution.