  A nearest neighbour spin pair of the quasi-two-dimensional three-state Potts
model interacts with the strength $J(>0)$ in the $xy$-plane and with $\lambda
J$ $(0\le \lambda \ll 1)$ in the $z$-axis. The phase transition is of
second-order when $\lambda = 0$ and is of first-order when $\lambda > 0$. The
dimensional crossover occurs with a change of the order of the phase
transition. We study the finite-size effects of the phenomenon by using a Monte
Carlo method with a multi-spin coding technique. The prediction of the
finite-size scaling theory is consistent with the Monte Carlo results.
