<p>To develop better non-destructive detection technology, we developed the Electrical Resistance Tomography(ERT) inverse algorithm research based on the L-BFGS method and implemented the ERT approach to detect the finite-volume targets electrical structure in the construction engineering field and other fields. Initially, we compared the forward calculation results with Adam’s forward calculation results, and, subsequently, we can see that the electric potential has recovered to a certain extent, indicating that the algorithm is effective. Next, the 3D inversion adopts the L-BFGS method based on unstructured grids. The L-BFGS inversion is a regularization inversion, which constrains the model space, adopts a new model smoothing strategy, derives the smoothness operator on the unstructured grid in the finite element, and introduces the L2 norm to define the smoothness of the model. The L-BFGS inversion method improves the inversion effect, which is mainly reflected in saving calculation space, accelerating calculation speed, and providing excellent imaging results. Furthermore, we used the MPI parallel algorithm to speed up the calculation. The accuracy of the algorithm is verified by the inversions of several theoretical models. The ERT algorithm is employed to reconstruct the three-dimensional conductivity distribution within the targets object. Several experiments demonstrate that the ERT method can both locate and image steel bar in concrete, and demonstrate that it is possible to estimate the location of cracks or other insulators (e.g. the plastic plates) in concrete. Besides, the algorithm embodies the advantage that a finite-volume targets can be observed on any surface.</p>