On the Tibetan Plateau, the limited ground-based rainfall information owing to a harsh environment has brought great challenges to hydrological studies. Satellite-based rainfall products, which allow for a better coverage than both radar network and rain gauges on the Tibetan Plateau, can be suitable alternatives for studies on investigating the hydrological processes and climate change. In this study, a newly developed daily satellite-based precipitation product, termed Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks-Climate Data Record (PERSIANN-CDR), is used as input for a hydrologic model to simulate streamflow in the upper Yellow and Yangtze River basins on the Tibetan Plateau. The results show that the simulated streamflows using PERSIANN-CDR precipitation and the Global Land Data Assimilation System (GLDAS) precipitation are closer to observation than that using limited gauge-based precipitation interpolation in the upper Yangtze River basin. The simulated streamflow using gauge-based precipitation are higher than the streamflow observation during the wet season. In the upper Yellow River basin, gauge-based precipitation, GLDAS precipitation, and PERSIANN-CDR precipitation have similar good performance in simulating streamflow. The evaluation of streamflow simulation capability in this study partly indicates that the PERSIANN-CDR rainfall product has good potential to be a reliable dataset and an alternative information source of a limited gauge network for conducting long-term hydrological and climate studies on the Tibetan Plateau.