We theoretically investigate optical refraction behavior in a fluid system which contains silica-coated gold nanorods dispersed in silicone oil under an external electric field. Because of the formation of a chain-like or lattice-like structure of dispersed nanorods along the electric field, the fluid shows a hyperbolic equifrequency contour characteristic and, as a result, all-angle broadband optical negative refraction for transverse magnetic wave propagation can be realized. We calculate the effective permittivity tensor of the fluid and verify the analysis using finite element simulations. We also find that the negative refractive index can vary with the electric field strength and external field distribution. Under a non-uniform external field, the gradient refraction behavior can be realized.