  In this paper, resonances are introduced to a class of quantum walks on
$\mathbb{Z}$. Resonances are defined as poles of the meromorphically extended
resolvent of the unitary time evolution operator. In particular, they appear
inside the unit circle. Some analogous properties to those of quantum
resonances for Schr\"odinger operators are shown. Especially, the resonance
expansion, an analogue of the eigenfunction expansion, indicates the long-time
behavior of quantum walks. The decaying rate, the asymptotic probability
distribution, and the weak limit of the probability density are described by
resonances and associated (generalized) resonant states. The generic simplicity
of resonances is also investigated.
