<p>This paper investigates the existence of traveling wave solutions for the Gardner equation and its spatiotemporal delay form. Special attention is paid to the existence of traveling wave solutions. Using bifurcation theory in dynamical systems, this article presents the bifurcation set, phase trajectory diagram of Gardner equation and analytical solutions under some constraint conditions on parameters. Based on the relationships between traveling wave solutions and orbits of the corresponding ordinary differential equations, the persistence of solitary, kink and anti-kink wave solutions for the Gardner equation with a specific convolution kernel is investigated by using geometric singular perturbation theory, invariant manifold theory, and the Melnikov method. Moreover, under certain parameter conditions, some traveling wave solutions persist while others do not persist when the average delay is sufficiently small. Numerical simulations further verify the effectiveness of results.</p>