  In a paper from 1954, Marstrand proved that if $K\subset \mathbb{R}^2$ with
Hausdorff dimension greater than 1, then its one-dimensional projection has
positive Lebesgue measure for almost-all directions. In this article, we show
that if $M$ is a simply connected surface with non-positive curvature, then
Marstrand's theorem is still valid.
