In Kenig and Stein (Math Res Lett 6(1):1–15, 1999, https://doi.org/10.4310/MRL.1999.v6.n1.a1 ), the following type of multilinear fractional integral $$\begin{aligned} \int _{{\mathbb {R}}^{mn}} \frac{f_1(l_1(x_1,\ldots ,x_m,x))\cdots f_{m+1}(l_{m+1}(x_1,\ldots ,x_m,x))}{(|x_1|+\cdots +|x_m|)^{\lambda }} dx_1\ldots dx_m \end{aligned}$$ was studied, where $$l_i$$ are linear maps from $${\mathbb {R}}^{(m+1)n}$$ to $${\mathbb {R}}^n$$ satisfying certain conditions. They proved the boundedness of such multilinear fractional integral from $$L^{p_1}\times \cdots \times L^{p_{m+1}}$$ to $$L^q$$ when the indices satisfy the homogeneity condition. In this paper, we show that the above multilinear fractional integral extends to a linear operator for functions in the mixed-norm Lebesgue space $$L^{{\mathbf {p}}}$$ which contains $$L^{p_1}\times \cdots \times L^{p_{m+1}}$$ as a subset. Under less restrictions on the linear maps $$l_i$$ , we give a complete characterization of the indices $${\mathbf {p}}$$ , q and $$\lambda $$ for which such an operator is bounded from $$L^{{\mathbf {p}}}$$ to $$L^q$$ . And for $$m=1$$ or $$n=1$$ , we give necessary and sufficient conditions on $$(l_1, \ldots , l_{m+1})$$ , $${\mathbf {p}}=(p_1,\ldots , p_{m+1})$$ , q and $$\lambda $$ such that the operator is bounded.