In this paper we propose a simple high-gain type adaptive control scheme for Surge stabilization in a compression system. We consider a typical configuration in which the plenum throttle position is file control input, while the measured output is given by the total pressure at the compressor inlet. We prove convergence of the control scheme using a simplified, but widely accepted, second-order model. The system does not satisfy strict minimum-phase assumptions, usually introduced in the high-gain type adaptive control context, and therefore the proof has been tailored to the specific problem. We finally validate the proposed controller, by means of both numerical simulation and experiments on a real plant.