  In this paper, we consider the continuous limit of a nonlinear quantum walk
(NLQW) that incorporates a linear quantum walk as a special case. In
particular, we rigorously prove that the walker (solution) of the NLQW on a
lattice $\delta \mathbb Z$ uniformly converges (in Sobolev space $H^s$) to the
solution to a nonlinear Dirac equation (NLD) on a fixed time interval as
$\delta\to 0$. Here, to compare the walker defined on $\delta\mathbb Z$ and the
solution to the NLD defined on $\mathbb R$, we use Shannon interpolation.
