We investigate the quasi-equilibrium state of one-dimensional self-gravitating systems. If the null virial condition is satisfied at initial time, it is found that the number density around the center of the system at the quasi-equilibrium state has the universality similar to two-and three-dimensional self-gravitating systems reported in [1,2]. The reason why the null virial condition is sufficient for the universality is unveiled by the envelope equation. We present a phenomenological model to describe the universal structure by using a special Langevin equation with a distinctive random noise to self-gravitating systems. Additionally, we unveil a mechanism which decides the radius of the system.