To investigate localization in one-dimensional quasi-periodic nonlinear systems, we consider the Schrödinger equation $${\rm i}\dot{q}_n+\epsilon(q_{n+1}+q_{n-1})+V(n\tilde{\alpha}+x)q_n+ |q_n|^2q_n=0,\quad n\in\mathbb{Z},$$ i q ˙ n + ϵ ( q n + 1 + q n - 1 ) + V ( n α ~ + x ) q n + | q n | 2 q n = 0 , n ∈ Z , as a model, with V a nonconstant real-analytic function on $${\mathbb{R}/\mathbb{Z}}$$ R / Z , and $${\tilde{\alpha}}$$ α ~ satisfying a certain Diophantine condition. It is shown that, if $${\epsilon}$$ ϵ is sufficiently small, then for a.e. $${x\in\mathbb{R}/\mathbb{Z}}$$ x ∈ R / Z , dynamical localization is maintained for “typical” solutions in a quasi-periodic time-dependent way.