The structure and morphology of nanomateials strongly influence their nonlinear optical properties. In this work, we report a systematic investigation of second order nonlinear optical responses and their structural dependencies in the case of a plasmonically hybrid nanostructure, hollow gold nanoprisms (HGNs). The first hyperpolarizabilities (β) of the HGNs have been measured using the two-photon Rayleigh scattering (TPRS) technique. The measured hyperpolarizability values are extremely large for the HGNs, larger than those for gold nanospheres or gold nanorods with similar size and surface area. The larger β values of the HGNs are due to a strong local electromagnetic field enhancement owing to efficient plasmon hybridization. We find that the β values for the HGNs studied here have a purely local dipolar origin, as confirmed by their surface area dependence. Moreover, the SH responses of the HGNs are found to be a linear function of their aspect ratios. Our results suggest that the nonlinear optical (NLO) properties of HGNs can be tailor made and utilized to suit various practical applications.