We discuss the production of cosmic-ray (CR) nuclei in a supernova remnant (SNR). Especially, we take into account the spallation of CR nuclei inside the interstellar medium (ISM) or circumstellar medium (CSM) surrounding the SNR, as well as the acceleration and escape of secondarily produced CR nuclei such as Li, Be, and B. We find that if the SNR is surrounded by a dense CSM with a wind-like density profile ($\propto r^{-2}$), the spectra of the escaping secondary nuclei are harder than those of the escaping primary nuclei. If we consider the CRs from such an SNR located in the vicinity of the Earth ($\lesssim 2~{\rm kpc}$) in addition to the average Galactic CRs, we can reproduce the spectral hardening of CRs around $\sim 200~{\rm GV}$ and softening around $\sim 10~{\rm TeV}$, as well as the flattening of the B/C ratio above $\sim ~{\rm TeV}/{\rm n}$.