The extinction spectra and E field distribution of a U-shaped nanostructure have been calculated using the discrete dipole approximation method, and compared to those of the parallel-nanorod structure. For a parallel-nanorod structure, when light propagates with its E field perpendicular to the nanorod axis only transverse plasmon modes are excited. Under the same condition for a U-shaped nanostructure, because the bottom nanorod builds a path for the electrons oscillations, longitudinal mode plasmon oscillations can also occur along the vertical nanorods. A U-shaped nanostructure has more hot spots than a parallel-nanorod structure; and at the longitudinal mode incidence, the E field enhancements are much larger than those of the parallel-nanorod structure. The longitudinal mode plasmon peaks red shift linearly with increase in the height, and decay exponentially with increasing nanorod radius. When the separation between two vertical nanorods increases, the longitudinal mode plasmon peaks first blue shift and then red shift linearly. These results could be used to engineer U-shaped nanostructures for specific plasmonic applications.