We establish the existence of center manifolds for a class of non-uniformly partially hyperbolic trajectories of non-autonomous ordinary differential equations $v'=A(t)v+f(t,v)$ on Banach spaces. In particular, we allow the stable and unstable components of $v'=A(t)v$ to exhibit non-uniform contraction and expansion along the trajectory. We also allow the center component to exhibit non-uniform behavior. To the best of our knowledge, we establish the first center manifold theorem in the non-uniform setting.