  Recently, Ban\~{a}dos, Silk and West (BSW) found that the center-of-mass
energy of two colliding test particles in the neighborhood of an extreme Kerr
black hole could be arbitrarily high when one particle has the critical angular
momentum $L_\text{C}$. In their paper, they considered the black holes living
in a Minkowski space-time with a zero cosmological constant. In this work, we
study this process of particles in the backgrounds of the Kerr black holes
living in a space-time with a nonzero cosmological constant. We find that for
kerr black holes living in a space-time with a negative cosmological constant
(Kerr-anti-de Sitter black holes), this process of particles could happen only
if the Kerr-anti-de Sitter black hole is extreme and an additional fine tuning
is satisfied; while for kerr black holes living in a space-time with a positive
cosmological constant (Kerr-de Sitter black holes), this process of particles
could happen no matter the Kerr-de Sitter black hole is extreme or not. We also
study the particle collision outside the outer horizon of the Kerr-(anti-) de
Sitter black hole in some cases. We find that there is a possibility that we
could tune one colliding particle's angular momentum to gain the large
center-of-mass energy without increase the particle's energy.
