Phase distribution within an annular channel is desired to know in cooling systems. Electrical resistance tomography (ERT) is a promising technique to achieve this task in a noninvasive and visualized manner. However, high nonlinearity and ill condition of ERT restrict its spatial resolution. The internal structure that forms the annular channel with the pipe wall makes the image reconstruction of phase distribution different from the circular cross section that ERT usually applied to. In this paper, a hybrid solver coupling the finite-element method and boundary-element method is proposed to solve the forward problem more efficiently. This algorithm is based on an elaborately designed finite-element forward solution, which speeds up the image reconstruction by eliminating the unknowns inside the known internal structure using boundary element method. The Levenberg-Marquardt (L-M) method is used to achieve a fast convergence and a high numerical accuracy and then to reconstruct the phase distribution within the annular channel. The linear and nonlinear forms of the L-M methods are compared in the cases of changing the internal structure conductivity, in order to understand the influence of the internal structure.