  The Epoch of Reionization (EoR) neutral Hydrogen (HI) 21-cm signal evolves
significantly along the line-of-sight (LoS) due to the light-cone (LC) effect.
It is important to accurately incorporate this in simulations in order to
correctly interpret the signal. 21-cm LC simulations are typically produced by
stitching together slices from a finite number $(N_{\rm RS})$ of ''reionization
snapshot'', each corresponding to a different stage of reionization. In this
paper, we have quantified the errors in the 21-cm LC simulation due to the
finite value of $N_{\rm RS}$. We show that this can introduce large
discontinuities $(> 200 \%)$ at the stitching boundaries when $N_{\rm RS}$ is
small $(= 2,4)$ and the mean neutral fraction jumps by $\delta \bar{x}_{\rm HI}
= 0.2,0.1$ respectively at the stitching boundaries. This drops to $17 \%$ for
$N_{\rm RS} = 13$ where $\delta \bar{x}_{\rm HI}=0.02$. We present and also
validate a method for mitigating this error by increasing $N_{\rm RS}$ without
a proportional increase in the computational costs which are mainly incurred in
generating the dark matter and halo density fields. Our method generates these
fields only at a few redshifts, and interpolates them to generate reionization
snapshots at closely spaced redshifts. We use this to generate 21-cm LC
simulations with $N_{\rm RS} = 26,51,101$ and $201$, and show that the errors
go down as $N_{\rm RS}^{-1}$.
