  A mixed function is a real analytic map $f\colon \mathbb{C}^n \to \mathbb{C}$
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 $\mathbf{0}$ on real
analytic varieties $V_f:=f^{-1}(0)$ defined by mixed functions $f$ with
isolated critical point at $\mathbf{0}$. We call this index the mixed GSV-index
and it generalizes the classical GSV-index defined by Gomez-Mont, Seade and
Verjovsky, 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. As applications we prove that the mixed GSV-index is equal
to the Poincar\'e-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 $\frac{f}{\|f\|}\colon \mathbb{S}_\epsilon \setminus L_f \to \mathbb{S}^1$
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 based on the
curvatura integra defined by Kervaire.
