In this paper we adopt a new approach-the evolutionary algorithm based on cell division operation-to deal with ground-state energies of double-electron systems. This algorithm is based on the evolution of sets and can incorporate other search algorithms. Firstly, we make a search for several good subsets of solution space at the same time. Then, we make a fine search in the neighbourhood of some better points obtained in the first step to determine the final optimal results. In addition, the cell division enables the solution subspaces to become smaller and smaller, and thus increase the convergence speed. We have tested this approach on double-electron systems in magnetic fields, and the results obtained have shown that it can improve not only the efficiency but also the accuracy of the calculations compared with other methods.