Sucrose metabolism in roots of metallophytes is very important for root growth and maintenance of heavy metal tolerance. However, rare researches have been carried out on this topic so far. We tested here a hypothesis that roots of copper-tolerant plants should manifest higher activities of sucrose-cleaving enzymes than non-tolerant plants for maintaining root growth under Cu stress. Plants of two contrasting populations of metallophyte Rumex dentatus, one from an ancient Cu mine (MP) and the other from a non-mine site (NMP), were treated with Cu in controlled experiments. Cu treatment resulted in a higher root biomass and root/shoot biomass ratio in MP compared to NMP. More complicated root system architecture was showed in MP under Cu stress. Activities and transcript levels of acid invertase as well as contents of sucrose and reducing sugar in MP were elevated under Cu treatment, while activities of neutral/alkaline invertase and sucrose synthase showed no significant differences between two populations. The results indicate important roles of acid invertase in governing root growth under Cu stress.