We consider a parameter identification problem associated with a quasi-linear elliptic Neumann boundary value problem involving a parameter function a(⋅) and the solution u(⋅), where the problem is to identify a(⋅) on an interval $I:= g(\G)$ from the knowledge of the solution u(⋅) as g on $\G$, where $\G$ is a given curve on the boundary of the domain $\O\subseteq \R^3$ of the problem and g is a continuous function. The inverse problem is formulated as a problem of solving an operator equation involving a compact operator depending on the data, and for obtaining stable approximate solutions under noisy data, a new regularization method is considered. The derived error estimates are similar to, and in certain cases better than, the classical Tikhonov regularization considered in the literature in the recent past.