Light-matter interactions driven by ultrahigh-intensity lasers have great potential to uncover the physics associated with quantum electrodynamics (QED) processes occurring in neutron stars and black holes. The Compton scattering between an ultra-relativistic electron beam and an intense laser can reveal a new interaction regime, known as strong-field QED. Here we present an experimental demonstration of nonlinear Compton scattering in a strong laser field, in which a laser-accelerated multi-gigaelectronvolt electron scatters off hundreds of laser photons and converts them into a single gamma-ray photon with several-hundred-megaelectronvolt energy. Along with particle-in-cell (PIC)-QED simulations and analytical calculations, our experimental measurement of gamma-ray spectra verifies the occurrence of Compton scattering in the strongly nonlinear regime, paving the road to examine nonlinear Breit-Wheeler pair production and QED cascades. Researchers demonstrate nonlinear Compton scattering in a strong laser field, in which a laser-accelerated multi-GeV electron scatters off hundreds of laser photons and converts them into a single gamma-ray photon with several-hundred-MeV energy.