An initially two-dimensional grid of elastic rods may be actuated into a three-dimensional shell-like structure, through buckling, when the end-points of the rods are constrained to a shrunk boundary. The shape of the 3D gridshell is a joint result of elasticity and geometric constraint. We develop a discrete differential geometry-based model of elastic gridshell to investigate their form-finding process. Even though the forward process from 2D footprint to 3D gridshell can be captured by physics-based simulation, the inverse problem of obtaining the original footprint given the 3D deformed shape still lacks a generalized method. In this paper, we propose a genetic algorithm (GA)-based inverse design method to explore the planar footprint of an elastic gridshell as well as the corresponding geometric constraints. Geometric features extracted from the original planar form are encoded into various chromosomes to constitute a population in every generation. With the fitness function constructed based on the deviation of the candidate solution from the 3D target shape, the population evolves gradually until the individual of the smallest fitness value representing the optimal footprint and final boundary constraints is found under seven predefined geometric constraints. Given a series of representative target shapes, e.g., hemispherical cap, paraboloid structure, Gaussian curve shape, and semi-ellipsoid, their original footprints are quantified using a network of 10 elastic rods. Excellent agreement is obtained between the prescribed 3D shape and the simulated buckled structures as small fitness value is obtained and little difference between them is observed, which validates the effectiveness of the proposed GA-based inverse design method.