  In the framework of the deformed quantum mechanics with minimal length, we
consider the motion of a non-relativistic particle in a homogeneous external
field. We find the integral representation for the physically acceptable wave
function in the position representation. Using the method of steepest descent,
we obtain the asymptotic expansions of the wave function at large positive and
negative arguments. We then employ the leading asymptotic expressions to derive
the WKB connection formula, which proceeds from classically forbidden region to
classically allowed one through a turning point. By the WKB connection formula,
we prove the Bohr-Sommerfeld quantization rule up to $\mathcal{O}(\beta)$. We
also show that, if the slope of the potential at a turning point is too steep,
the WKB connection formula fall apart around the turning point.
