This study deals with the use of conjugate gradient method in conjunction with an adjoint problem formulation for the estimation of an unknown coefficient in a boundary value problem (BVP) of second-order. in the present approach, no a priori assumption is required regarding the functional form of the unknown. The accuracy of the inverse analysis is examined by simulated exact and inexact data. The numerical results show that good estimation on unknown coefficient can be obtained for all the test cases considered in this study.