We investigate the quench dynamics of the one-particle entanglement spectra (OPES) for systems with topologically nontrivial phases. By using dimerized chains as an example, it is demonstrated that the evolution of OPES for the quenched bipartite systems is governed by an effective Hamiltonian which is characterized by a pseudospin in a time-dependent pseudomagnetic field S(k,t). The existence and evolution of the topological maximally entangled states (tMESs) are determined by the winding number of S(k,t) in the k-space. In particular, the tMESs survive only if nontrivial Berry phases are induced by the winding of S(k,t). In the infinite-time limit the equilibrium OPES can be determined by an effective time-independent pseudomagnetic field Seff(k). Furthermore, when tMESs are unstable, they are destroyed by quasiparticles within a characteristic timescale in proportion to the system size.