  In this work we focus on a toy model: (3+1)-dimensional Ho\v{r}ava-Lifshitz
gravity coupling with an anisotropic electromagnetic (EM) field which is
generated through a Kaluza-Klein reduction of a (4+1)-dimensional
Ho\v{r}ava-Lifshitz gravity. This model exhibits a remarkable feature that it
has the same velocity for both gravitational and electromagnetic waves. This
feature makes it possible to restrict the parameters of the theory from GRB
170817A. In this work we use this feature to discuss possible constraints on
the parameter $\beta$ in the theory, by analyzing the possible Lorentz
invariance violation effect of the GRB 170817A. This is achieved by analyzing
potential time delay of gamma-ray photons in this event. It turns out that it
places a stringent constraint on this parameter. In the most ideal case, it
gives $|1-\sqrt{\beta}|<(10^{-19}-10^{-18})$.
