The potential distribution of the invasive plant Anredera cordifolia (Tenore) Steenis was predicted by Random Forest models under current and future climate-change pathways (i.e., RCP4.5 and RCP8.5 of 2050s and the 2070s). Pearson correlations were used to select variables; the prediction accuracy of the models was evaluated by using AUC, Kappa, and TSS. The results show that suitable future distribution areas are mainly in Southeast Asia, Eastern Oceania, a few parts of Eastern Africa, Southern North America, and Eastern South America. Temperature is the key climatic factor affecting the distribution of A. cordifolia. Important metrics include mean temperature of the coldest quarter (0.3 • C ≤ Bio11 ≤ 22.9 • C), max temperature of the warmest month (17.1 • C ≤ Bio5 ≤ 35.5 • C), temperature annual range (10.7 • C ≤ Bio7 ≤ 33 • C), annual mean air temperature (6.8 • C ≤ Bio1 ≤ 24.4 • C), and min temperature of coldest month (−2.8 • C ≤ Bio6 ≤ 17.2 • C). Only one precipitation index (Bio19) was important, precipitation of coldest quarter (7 mm ≤ Bio19 ≤ 631 mm). In addition, areas with strong human activities are most prone to invasion. This species is native to Brazil, but has been introduced in Asia, where it is widely planted and has escaped from cultivation. Under the future climate scenarios, suitable habitat areas of A. cordifolia will expand to higher latitudes. This study can provide a reference for the rational management and control of A. cordifolia.