Metabolic flux distribution is determined by the physiological state of a cell under specific growth conditions, revealing which participating reactions are active and how the fluxes through these reactions describe the physiological state of the cell. One approach to studying metabolic flux distribution is elementary flux mode (EFM) analysis, which decomposes complex metabolic flux distributions into a set of EFMs called active EFMs. However, the challenge lies in figuring out how to allocate weight factors to EFMs reasonably and eliminate biochemically infeasible EFMs to make the reconstructed flux distribution closer to the actual physiological state. In this paper, we propose a novel method called Genome-scale Enzyme Mass Minimization Decomposition (gEMMD) for identifying active EFMs. Our method calculates EFMs that include selected reactions and conform to the flux distribution. Employing a depth-first search strategy, it explores the local solution space, starting with the EFM of the lowest enzyme mass, without computing all EFMs in the genome-scale metabolic network. We applied it to the core Escherichia coli metabolic network, demonstrating the effectiveness of our method and showing that the active EFM combinations identified by gEMMD have high growth rate and thermodynamically favorable. Moreover, our results suggest that gEMMD can effectively identify key active EFMs. Finally, we studied the growth of the iAF1260 genome-scale metabolic network in Luria-Bertani (LB) medium containing different carbon sources, revealing carbon source contributions not evident in the observed flux distribution. gEMMD thus could be a promising complement to the existing flux decomposition tools.