The effects of climate change and of land use/cover change (LUCC) on streamflow as demonstrated by hydrological models are pressing issues on the frontiers of global environmental change research. The Nandu River Basin (NRB) as the largest of three river basins on the tropical Hainan Island, China, is subjected to an analysis of streamflow response to climate and to land-use change. It is based on the Soil and Water Assessment Tool (SWAT) coupled with climate change signals extracted from the global climate model data in the Coupled Model Intercomparison Project Phase 6 (CMIP6) and with land-use change scenarios modeled by Cellular Automata (CA)—Markov. The results are summarized as follows: (1) Climate change contributed more to streamflow change than land-use change in the NRB, with contributions of 97.57% and 2.43%, respectively. Precipitation and temperature were the most important climate variables, contributing 92.66% and 4.91% to streamflow change. (2) In the tropical island basin from 1990 to 2015, LUCC regulated the hydrological processes in the NRB and affected hydrological processes by increasing evapotranspiration and decreasing surface runoff and subsurface flow, which resulted in decreasing streamflow. (3) Under the climate change and land-use change scenarios of the near-term period (2021–2040), the annual streamflow decreased as during the reference period (1995–2014); particularly, it decreased most (−6.16%) on the SSP126 path. These results present a case study for understanding the hydrological cycle of tropical island basins and to provide a theoretical basis for water resources management and regional sustainable development of tropical islands.