Satellite remote sensing of chlorophyll-a (Chl-a) provides the only continuous global-scale monitoring of phytoplankton abundance for over two decades. While certain trends have been observed in the satellite Chl-a data, it remains uncertain whether the changes are attributable to climate warming, because the data is not long enough to separate the role of climate warming from natural variability. Here, using a deep-learning model trained with an ensemble of 10 Earth System Model (ESM) simulations, we identified the climate-warming signal in satellite-derived global Chl-a fields. By comparison, a null model trained on ESM simulations forced only by natural variability was unable to identify a warming signal, confirming the role of climate warming. The warming signal is primarily derived from the spatial pattern of global Chl-a trends, and eastern and western boundary regions are most sensitive to warming. Our results explicitly reveal the ongoing climate-warming effect on global marine phytoplankton this century.