In this talk we derive a new Minkowski-type inequality for closed convex surfaces in the hyperbolic 3-space. The inequality is obtained by explicitly computing the area of the family of surfaces arising from the normal flow and then applying the isoperimetric inequality. Using the same method, we also we give elementary proofs of the classical Minkowski inequalities for closed convex surfaces in the Euclidean 3-space and in the 3-sphere.