We studied the demography of a subpopulation of African elephants Loxodonta africana in Tarangire National Park, Tanzania, from 1993 to 2005. The Tarangire elephants had been affected by heavy poaching prior to 1993. We monitored 668 individually known elephants in 27 family groups. The population increased from 226 to 498 individuals, with mean group size increasing from 8.4 to 18.3. The average annual growth rate was 7.1% (range 2.0–16.9%). This approaches the maximal growth rate for African elephants, with corresponding minimal values for demographic parameters. The mean interbirth interval was 3.3 years, mean age of first reproduction 11.1 years, average annual mortality of elephants younger than 8 years 3%, and average annual mortality of adult females 1%. Probability of conceiving was positively correlated with annual rainfall. No significant density-dependent effects were recorded. Rapid growth was aided by high rainfall, low population density and release from the stresses of poaching. These results demonstrate that elephant populations are capable of rapid population increases for extended periods of time given the right ecological and social conditions. This has consequences for elephant conservation and management.