  We report a comprehensive high-pressure study on the antiferromagnetic
topological insulator EuSn2As2 up to 21.1 GPa through measurements of
synchrotron x-ray diffraction, electrical resistance, magnetic resistance, and
Hall transports combined with first-principles calculations. No evident trace
of a structural phase transition is detected. The Neel temperatures determined
from resistance are increased from 24 to 77 K under pressure, which is resulted
from the enhanced magnetic exchange couplings between Eu2+ ions yielded by our
first-principles calculations. The negative magnetoresistance of EuSn2As2
persists to higher temperatures accordantly. However, the enhancement of the
observed N\'eel temperatures deviates from the calculations obviously above
10.0 GPa. In addition, the magnitude of the magnetoresistance, the Hall
coefficients, and the charge carrier densities show abrupt changes between 6.9
to 10.0 GPa. The abrupt changes probably originate from a pressure induced
valence change of Eu ions from a divalent state to a divalent and trivalent
mixed state. Our results provide insights into variation of the magnetism of
EuSn2As2 and similar antiferromagnetic topological insulators under pressure.
