  We consider a class of parabolic nonlocal $1$-Laplacian equation
\begin{align*} u_t+(-\Delta)^s_1u=f \quad \text{ in }\Omega\times(0,T].
\end{align*} By employing the Rothe time-discretization method, we establish
the existence and uniqueness of weak solutions to the equation above. In
particular, different from the previous results on the local case, we infer
that the weak solution maintains $\frac{1}{2}$-H\"{o}lder continuity in time.
