A linear map $${\phi}$$ of operator algebras is said to preserve numerical radius (or to be a numerical radius isometry) if $${w(\phi(A))=w(A)}$$ for all A in its domain algebra, where w(A) stands for the numerical radius of A. In this paper, we prove that a surjective linear map $${\phi}$$ of the nest algebra $${{\rm Alg}\mathcal N}$$ onto itself preserves numerical radius if and only if there exist a unitary U and a complex number ξ of modulus one such that $${\phi(A)= \xi UAU^*}$$ for all $${A\in{\rm Alg}\mathcal N}$$ , or there exist a unitary U, a conjugation J and a complex number ξ of modulus one such that $${\phi(A)=\xi UJA^*JU^*}$$ for all $${A\in{\rm Alg}\mathcal N}$$ .