<p>The Legendre spectral discretization of evolutionary differential equations in time serves as a natural counterpart to its spatial counterpart, offering high-order accuracy with relatively few degrees of freedom. Its global nature leads to an all-at-once system in which all temporal unknowns must be solved simultaneously, posing significant computational challenges. In this paper, we propose a novel parallel-in-time preconditioner for such systems, enabling each preconditioned step to be solved efficiently in a time-parallel manner. The preconditioner is constructed by discretizing a modified periodic system that retains the structure of the original evolution equation but replaces the initial condition with a periodic-like condition. Spectral analysis shows that the eigenvalues of the preconditioned system are tightly clustered, and the preconditioned GMRES algorithm achieves linear convergence. Numerical experiments confirm the effectiveness of the proposed preconditioner and demonstrate its competitiveness compared to existing preconditioners in the literature.</p>