  The ground state magnetization curve around the critical magnetic field $H_c$
of quantum spin chains with the spin gap is investigated. We propose a size
scaling method to estimate the critical exponent $\delta$ defined as $m\sim
|H-H_c|^{1/\delta}$ from finite cluster calculation. The applications of the
method to the S=1 antiferromagnetic chain and S=1/2 bond alternating chain lead
to a common conclusion $\delta =2$. The same result is derived for both edges
of the magnetization plateau of the S=3/2 antiferromagnetic chain with the
single ion anisotropy.
