We have studied a dimensional crossover of a diffusion-limited reaction A + B --> 0, with and without a drift in a quasi-one-dimensional lattice W x L where the length of the lattice L is large and W is the width of the lattice. The density follows a scaling function such as C(t)similar toW(-x)f(t/t(c)), where f(z)similar toz(-alpha),z much less than1 with alpha = 0.59(1) regardless of the drift and f(z)similar toz(-beta),z much greater than1 with beta = 0.254(8) without the drift and beta = 0.31(2) with the drift. We found the scaling exponent x = 0.87(1) for the isotropic diffusion and x = 1.05( 1) for the maximum drift. We observed that the crossover time had a power law like t(c)similar toW(y) with y = 1/2(beta - alpha).