Let $\omega$ be a Kähler form on a projective algebraic manifold X. Then there exists $A\geq 1$ such that for every $\varphi\in PSH(X,\omega)$, we can find $\varphi_{j}\in PSH(X,A\omega)\cap{\mathcal{C}}^{\infty}(X)$ which decrease towards $\varphi$.