  We propose a scheme to implement the quantum walk for SU(1,1) in the phase
space, which generalizes those associated with the Heisenberg-Weyl group. The
movement of the walker described by the SU(1,1) coherent states can be
visualized on the hyperboloid or the Poincar\'{e} disk. In both one-mode and
two-mode realizations, we introduce the corresponding coin-flip and
conditional-shift operators for the SU(1,1) group, whose relations with those
for Heisenberg-Weyl group are analyzed. The probability distribution, standard
deviation and the von Neumann entropy are employed to describe the walking
process. The nonorthogonality of the SU(1,1) coherent states precludes the
quantum walk for SU(1,1) from the idealized one. However, the overlap between
different SU(1,1) coherent states can be reduced by increasing the Bargmann
index $k$, which indicates that the two-mode realization provides more
possibilities to simulate the idealized quantum walk.
