The AdS soliton spacetime is a vacuum static solution of five-dimensional Einstein equations with a cosmological constant. It is asymptotically AdS and regular everywhere without having any curvature singularity or an event horizon inside. Recently, Horowitz and Myers conjectured that this spacetime is the ground state among all spacetime solutions that are asymptotically AdS. If such a conjecture is valid, the spacetime should be stable under small perturbations. We have investigated this issue by numerically studying the full nonlinear evolution of a certain class of perturbations.