Liquid propelled rocket engines (LPRE) are highly non-linear systems that require complex stability analysis and regulation. Most often, this is performed by linearizing in the neighborhood of a functioning point which makes it difficult to account for changes of points e.g. for reusable launchers. In this paper the objective is to propose a non linear control law to regulate the thrust of the engine, which is represented by the reaction chamber pressure, and the mixture ratio between the fuel and the oxidizer. This control law must provide stability guarantees for the system for a variety of functioning points. The new design is based on Contraction theory and is shown to address both stability and regulation objectives as illustrated with simulation results.