In an earlier paper , the effect of the nearby known supernova remnants ( SNRs ) on the local cosmic-rays ( CRs ) was studied , considering different possible forms of the particle injection time . The present work is a continuation of the previous work , but assumes a more realistic model of CR propagation in the Galaxy . The previous work assumed an unbounded three-dimensional diffusion region , whereas the present one considers a flat cylindrical disc bounded in both the radial and vertical directions . The study has found that the effect of the vertical halo boundary H on the local SNR contribution to the observed CR anisotropy is negligible as long as H \gtrsim 2 kpc . Considering the values of the halo height H \gtrsim 2 kpc obtained by different authors , the present work suggests that the study of the effect of local sources on the CR anisotropy can be carried out without having much information on H and hence , using the much simpler three-dimentional unbounded solution . Finally , the present work discusses about the possibility of explaining the observed anisotropy below the knee by a single dominant source with properly chosen source parameters , and claims that the source may be an undetected old SNR with a characteristic age of \sim 1.5 \times 10 ^ { 5 } yr located at a distance of \sim 0.57 kpc from the Sun .