Let S n [f] be the nth partial sum of the orthonormal polynomials expansion with respect to a Freud weight. Then we obtain sufficient conditions for the boundedness of S n [f] and discuss the speed of the convergence of S n [f] in weighted L p space. We also find sufficient conditions for the boundedness of the Lagrange interpolation polynomial L n [f], whose nodal points are the zeros of orthonormal polynomials with respect to a Freud weight. In particular, if W(x)=e - ( 1 / 2 ) x 2 is the Hermite weight function, then we obtain sufficient conditions for the inequalities to hold: (S n [f]-f) ( k ) Wu b L p ( R ) =<C1n r - k f ( r ) Wu B L p ( R ) a nd (L n [f]-f) ( k ) Wu b L p ( R ) =<C1n r - k f ( r ) W(1+x 2 ) r / 3 u B L p ( R ) ,where u γ (x)=(1+|x|) γ ,γ R and k=0,1,2...,r.