A mixed function is a real analytic map \(f:\mathbb {C}^n\rightarrow \mathbb {C}\) in the complex variables \(z_1,\dots ,z_n\) and their conjugates \(\bar{z}_1,\dots ,\bar{z}_n\) . In this article, we define an integer valued index for vector fields v with isolated singularity at \(\textbf{0}\) on real analytic varieties \(V_f:=f^{-1}(0)\) defined by mixed functions f with isolated critical point at \(\textbf{0}\) . We call this index the mixed GSV index and it generalizes the classical GSV index defined by Gomez-Mont, Seade and Verjovsky in (Math Ann 291(4):737–751, 1991), i.e., if the function f is holomorphic, then the mixed GSV index coincides with the GSV index. Furthermore, the mixed GSV index is a lifting to \(\mathbb {Z}\) of the \(\mathbb {Z}_2\) -valued real GSV index defined by Aguilar, Seade and Verjovsky in Aguilar et al. (J Reine Angew Math 504:159–176, 1998). As applications, we prove that the mixed GSV index is equal to the Poincaré–Hopf index of v on a Milnor fiber. If f also satisfies the strong Milnor condition, i. e., for every \(\epsilon >0\) (small enough), the map \(\frac{f}{\Vert f\Vert }:\mathbb {S}_\epsilon {\setminus } L_f \rightarrow \mathbb {S}^1\) is a fiber bundle, we prove that the mixed GSV index is equal to the curvatura integra of f defined by Cisneros-Molina, Grulha and Seade in (Int J Math 25(7): 1450069, 2014) based on the curvatura integra defined by Kervaire in (Courbure integrale generalisee et homotopie., Mathematische Annalen, pp. 219–252, 1956).
