The Dual Reciprocity Boundary Element Method and the Conjugate Gradient Method are proposed to identify the geometry shape of two-dimensional steady-state heat conduction problem with the heat source.Firstly,the DRM is used to transform the domain integral of heat source into boundary integral.Therefore the pure boundary integral equation is obtained which can avoid discretizing the considered domain of the problem.Then the objective function is optimized by the Conjugate Gradient Method.Meanwhile,the sensitivity and adjoint problems are considered to select the search step length and to compute the gradient of the corresponding function.Finally,the effects of the initial guesses and the measured errors on the accuracy of inverse solutions are discussed.Numerical examples are given to demonstrate the stability and effectivity of this method.