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Molecular surface plasmon resonance (SPR) sensing is one of the most common applications of an array of periodic nanoholes in a metal film. However, metallic nanohole arrays (NHAs) with low-hole count have lower resolution and SPR sensing performance compared to NHAs with high-hole count. In this paper, we present a compact three-dimensional (3D) plasmonic nanostructure with extraordinary optical transmission properties benefiting from surface plasmon matching and enhanced localized surface plasmon coupling. The 3D nanostructure consisted of a gold film containing a NHA with an underlying cavity and a gold nanocone array (NCA) at the bottom of the cavity. Each nanocone was aligned with the nanohole above and the truncated apex of each nanocone was in close proximity (100 nm) to the gold film. The NHA-NCA structures outperformed conventional NHA structures in terms of bulk sensitivity and Figure of Merit (FOM). Furthermore, the NHA-NCA structure with 525-nm periodicity was capable of sensing streptavidin down to 2 nM exhibiting a 10-fold increase in streptavidin sensitivity compared to conventional NHA structures. The sensitivity and performance of the 3D nanostructure can be further improved by exploiting multiplexing methods in combination with stable light sources and detection systems.