  In this paper, we study the spin chain and string excitation in the
two-parameters $q$-deformed AdS$_3\times$S$^3$ proposed by Hoare. We obtain the
deformed spin chain model at the fast spin limit for choices of deformed
parameters. General ansatz for giant magnons are studied in great detail and
complicated dispersion relation is treated perturbatively. We also study
several types of hanging string solutions and their charges and spins are
analyzed numerically. At last, we explore its pp-wave limit and find its
solution only depends on the difference of deformed parameters.
