  A $C^2$ function on $\mathbb{R}^n$ is called strictly $(n-1)$-convex if the
sum of any $n-1$ eigenvalues of its Hessian is positive. In this paper, we
establish a global $C^2$ estimates to the Monge-Amp\`ere equation for strictly
$(n-1)$-convex functions with Neumann condition. By the method of continuity,
we prove an existence theorem for strictly $(n-1)$-convex solutions of the
Neumann problems.
