In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type \begin{equation*} u(x)=\overrightarrow{l}+C_{*}\int_{\mathbb{R}^n}\frac{(1-|u(y)|^2)|u(y)|^2u(y)-\frac{1}{2}(1-|u(y)|^2)^2u(y)}{|x-y|^{n-\alpha}}dy. \end{equation*} Here $u:\mathbb{R}^n\rightarrow \mathbb{R}^k$ is a bounded, uniformly continuous function with $k\geqslant1$ and $0<\alpha