We present the experimental results which show $\phi$-meson mass modification at normal nuclear density. The aim of our experiment, KEK-PS E325, is to detect possible in-medium modification of vector mesons via the reaction 12GeV/c $p+A \to \rho, \omega, \phi + X \to e^+e^- + X'$. Modification of mass spectral function of vector meson, even at normal nuclear density, have been suggested by many theories as a precursor of the QCD chiral phase transition. We used C and Cu targets as small and large target nuclei. In the high $\beta \gamma$ region, both results obtained for C and Cu targets were consistent with the simulation shape which included no spectral modification. On the other hand, in the low $\beta \gamma$ region, significant enhancement on the low-mass side of the $\phi$ meson peak was observed in the Cu data. Since slowly moving mesons in a larger nucleus have a larger probability of decaying inside a nucleus, this results suggest $\phi$ meson modification in a nucleus.