Summary: We consider a parameter identification problem associated with a quasilinear elliptic Neumann boundary value problem involving a parameter function \(a (\cdot)\) and the solution \(u (\cdot),\) where the problem is to identify \(a (\cdot)\) on an interval \(I:=g (\Gamma)\) from the knowledge of the solution \(u (\cdot)\) as \(g\) on \(\Gamma\), where \(\Gamma\) is a given curve on the boundary of the domain \(\Omega \subseteq \mathbb{R}^3\) 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 recent past.