We study the quasiparticle properties of a one-dimensional electron gas interacting with a long-range electron-electron interaction. The electron self-energy is calculated using the leading-order dynamical-screening approximation with (GWΓ approximation) and without the vertex corrections (GW approximation). The calculated one-electron properties such as the spectral function, damping rate, and also the momentum distribution indicate the significance of vertex corrections at low densities. ©2000 The American Physical Society.