The molecular distance geometry problem (MDGP) is a fundamental problem in determining molecular structures from the NMR data. We present a heuristic algorithm, the BetaMDGP, which outperforms existing algorithms for solving the MDGP. The BetaMDGP algorithm is based on the beta-complex, which is a geometric construct extracted from the quasi-triangulation derived from the Voronoi diagram of atoms. Starting with an initial tetrahedron defined by the centers of four closely located atoms, the BetaMDGP determines a molecular structure by adding one shell of atoms around the currently determined substructure using the beta-complex. The proposed algorithm has been entirely implemented and tested with atomic arrangements stored in an NMR format created from PDB files. Experimental results are also provided to show the powerful capability of the proposed algorithm.