Helium-bubble growth in \ensuremath{\alpha}-implanted palladium has been investigated by positron-lifetime measurements as a function of isothermal annealing time, t. The bubble radius shows first an expected ${\mathit{t}}^{1/6}$ variation and then an anomalous time dependence faster than ${\mathit{t}}^{1}$. It is shown that a model based on surface-diffusion-controlled migration and coalescence, taking into account the dependence of bubble diffusivity on the time-varying helium density in the bubble and ledge nucleation, explains the observed behavior.