In this paper, we aim to introduce and study the (locally strongly convex) equiaffine isoparametric functions on the affine space $$A^{n+1}$$, making the emphasis on their relation with the affine isoparametric hypersurfaces. Motivated by the case in the Euclidean space $$E^{n+1}$$, we first introduce the concept of equiaffine parallel hypersurfaces in $$A^{n+1}$$, and then equivalently re-define the equiaffine isoparametric hypersurfaces to be ones that are among families of equiaffine parallel hypersurfaces in $$A^{n+1}$$ of constant affine mean curvature. As the main result, we prove that an equiaffine isoparametric hypersurface is nothing but exactly a regular level set of some equiaffine isoparametric function.