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Knowing the stand age of rubber tree (Hevea brasiliensis) plantations is vitally important for best management practices, estimations of rubber latex yields, and carbon cycle studies (e.g., biomass, carbon pools, and fluxes). However, the stand age (as estimated from the establishment year of rubber plantation) is not available across large regions. In this study, we analyzed Landsat time series images from 1987–2015 and developed algorithms to identify (1) the establishment year of rubber plantations; and (2) the pre-conversion land cover types, such as old rubber plantations, evergreen forests, and cropland. Exposed soil during plantation establishment and linear increases in canopy closure during non-production periods (rubber seedling to mature plantation) were used to identify the establishment year of rubber plantations. Based on the rubber plantation map for 2015 (overall accuracy = 97%), and 1981 Landsat images since 1987, we mapped the establishment year of rubber plantations on Hainan Island (R2 = 0.85/0.99, and RMSE = 2.34/0.54 years at pixel/plantation scale). The results show that: (1) significant conversion of croplands and old rubber plantations to new rubber plantations has occurred substantially in the northwest and northern regions of Hainan Island since 2000, while old rubber plantations were mainly distributed in the southeastern inland strip; (2) the pattern of rubber plantation expansion since 1987 consisted of fragmented plantations from smallholders, and there was no tendency to expand towards a higher altitude and steep slope regions; (3) the largest land source for new rubber plantations since 1988 was old rubber plantations (1.26 × 105 ha), followed by cropland (0.95 × 105 ha), and evergreen forests (0.68 × 105 ha). The resultant algorithms and maps of establishment year and pre-conversion land cover types are likely to be useful in plantation management, and ecological assessments of rubber plantation expansion in China.