Invasive alien tree species can exert severe impacts, especially in insular biodiversity hotspots, but have been inadequately studied. Knowledge of the life history and population trends of an invasive alien tree species is essential for appropriate ecosystem management. The invasive tree Bischofia javanica has overwhelmed native trees on Haha-jima Island in the Ogasawara Islands, Japan. We explored forest community dynamics 2 years after a typhoon damaged the Sekimon primary forests on Haha-jima Island, and predicted the rate of population increase of B. javanica using a logistic model from forest dynamics data for 19 years. During the 2 years after the typhoon, only B. javanica increased in population size, whereas populations of native tree species decreased. Stem diameter growth of B. javanica was more rapid than that of other tree species, including native pioneer trees. Among the understory stems below canopy trees of other species, B. javanica grew most rapidly and B. javanica canopy trees decreased growth of the dominant native Ardisia sieboldii . These competitive advantages were indicated to be the main mechanism by which B. javanica replaces native trees. The logistic model predicted that B. javanica would reach 30% of the total basal area between 2017 (in the eastern plot adjacent to a former B. javanica plantation) and 2057 (in the western plot distant from the plantation site), which is a maximum percentage allowing to eradicate under the present guideline of the National Forest. The results suggest immediate removal of B. javanica is required to preserve native biodiversity in these forests.