We experimentally demonstrate the simultaneous enhancement of Raman and photoluminescence (PL) of core-shell hybrid nanoparticles consisting of Ag (core) and polydiacetylene (PDA, shell) through the assistance of localized surface plasmon (LSP) effect for the effective biosensor. Core-shell nanoparticles (NPs) are fabricated in deionized water through a sequential process of reprecipitation and self-assembly. The Raman signal of PDA on core-shell NPs is enhanced more than 100 times. Also, highly enhanced photoluminescence is observed on Ag/PDA hybrid NPs after coupling of the complementary t-DNA with p-DNA which are immobilized on PDA shell. This indicates that the core Ag affects the Raman and PL of PDA through the LSP resonance, which can be caused by the energy and/or charge transfer caused by the LSP coupling and the strong electromagnetic field near Ag NP surface. Only electrons present on the surface interact with the PDA shell, not involving the electrically neutral part of the electrons inside the Ag NP. Furthermore, this work shows that as prepared Ag/PDA NPs functionalized by probe DNA can sense the target DNA with an attomolar concentration (100 attomole).