Grain boundary relaxation at elevated temperatures in fine-grained pure magnesium and Mg-Al solid solutions was investigated by measuring damping capacity at low frequencies. A sharp increase in damping capacity caused by grain boundary relaxation was observed at above a certain temperature. The onset temperature depended on aluminum content; the onset temperature increased with aluminum content. It was demonstrated that aluminum was effective in suppressing grain boundary relaxation in magnesium alloys. However, additional measurement of the damping capacity of a dilute Mg-Y alloy revealed that yttrium was more effective in suppressing grain boundary relaxation.