The lowest-energy geometrical and electronic structures of Cu38 cluster are investigated by density-functional calculations combined with a genetic algorithm based on a many body semi-empirical interatomic potential, the traditional FCC-truncated Octahedron (OH) and an incomplete-Mackay icosahedron (IMI) are recognized as the two lowest energy structures (energetically degenerate isomers) but with different electronic structures: a semiconductor-type with the energy-gap of 0.356 eV for the IMI and a metallic-type with negligible gap for the OH, which is in good agreement with the experimental results. The electron affinity and ionization potential of Cu38 are also discussed and compared with the observations of the ultraviolet photoelectron spectroscopy experiments. The dynamical isomerization of the OH-like and IMI-like structures of Cu38 is revealed to dominate the pre-melting stage through the investigation by the molecular dynamics annealing simulations.