The one-dimensional expansion into vacuum of ion-electron plasma produced by laser ablation is investigated. The ions considered as an ideal fluid are governed by a fluid model where charge quasineutrality is assumed to prevail, while electron density follows a non-Maxwellian distribution. Showing that the expansion can be described by a self-similar solution, the resulting nonlinear Euler equations are solved numerically. It is found that the deviation of the electrons from Maxwellian distribution gives rise to new asymptotic solutions of physical interest affecting the density and velocity of plasma expansion.