In this paper, we investigate a Cauchy problem associated with Helmholtz-type equation in an infinite “strip”. This is a classical severely ill-posed problem, i.e., the solution (if it exists) does not depend continuously on the data (or Cauchy data), a small perturbation in the data can cause a dramatically large error in the solution for 0<x≤1. The stability of the solution is restored by using a wavelet regularization method. Moreover, some sharp stable estimates between the exact solution and its approximation in Hr(R)-norm is also provided and the numerical examples show that the method works effectively.