  We study antiferromagnetic two-leg spin-1/2 ladders with strong bond
randomness, using the real space renormalization group method. We find the
low-temperature spin susceptibility of the system follows non-universal power
laws, and the ground state spin-spin correlation is short-ranged. Our results
suggest that there is no phase transition when the bond randomness increases
from zero; for strong enough randomness the system is in a Griffith region with
divergent spin susceptibility and short-range spin-spin correlation.
