Given an amino acid sequence with the α-carbon 3D coordinates on its backbone, the all-atom protein backbone reconstruction problem (PBRP) is to rebuild the 3D coordinates of all major atoms (N, C and O atoms) on the backbone. In this paper, we first build a 4-residue fragment library extracted from PDB. Then, to solve PBRP, we search for fragments with similar structures based on the inner distances. To test the performance of our method, we use two testing sets of target proteins, one was proposed by Maupetit et al. and the other is a subset extracted from CASP7. We compare the experimental results of our method with three previous works, MaxSprout, Adcock's method and SABBAC proposed by Maupetit et al. The reconstruction accuracy of our method is comparable to these previous works. And the solution of our method is more stable than the previous works in most target proteins. These previous works contain complicated energy computation, while our method does not. Thus, our method requires much less execution time than the previous works.