Solid-state refrigeration offers potential advantages over traditional cooling systems, but few devices offer high specific cooling power with a high coefficient of performance (COP) and the ability to be applied directly to surfaces. We developed a cooling device with a high intrinsic thermodynamic efficiency using a flexible electrocaloric (EC) polymer film and an electrostatic actuation mechanism. Reversible electrostatic forces reduce parasitic power consumption and allow efficient heat transfer through good thermal contacts with the heat source or heat sink. The EC device produced a specific cooling power of 2.8 watts per gram and a COP of 13. The new cooling device is more efficient and compact than existing surface-conformable solid-state cooling technologies, opening a path to using the technology for a variety of practical applications.