The focal point of this paper is to develop a measure of closed-loop non-linearity. In this work, the Vinnicombe metric and the Quasi-Linear Parameter Varying representation of a non-linear system are exploited for this purpose. It is expected that the proposed measure can serve as a decision making tool for control engineers when considering whether a linear or a non-linear control strategy should be employed to close the loop for a non-linear system operating in a prescribed range.