We study the emission from an old supernova remnant (SNR) with an age of around 105 yrs and that from a giant molecular cloud (GMC) encountered by the SNR. When the SNR age is around 105 yrs, hadron acceleration is efficient enough to emit TeV γ-rays both at the shock of the SNR and that in the GMC. The maximum energy of primarily accelerated electrons is so small that TeV γ-rays and X-rays are dominated by hadronic processes, π 0-decay and synchrotron radiation from secondary electrons, respectively. However, if the SNR is older than several 105 yrs, there are few high-energy particles emitting TeV γ-rays because of the energy loss effect and/or the wave damping effect occurring at low-velocity isothermal shocks. It is found that the ratio of TeV γ-ray (1-10 TeV) to X-ray (2-10 keV) energy flux can be more than ～ 102. Such a source showing large flux ratio may be a possible origin of recently discovered unidentified TeV sources.