Most metallic glasses (MGs) exhibit weak evidence of slow β-relaxation in their dynamic mechanical spectroscopy spectra. In contrast to other MGs, the La-based MGs we report here show a distinct slow β-relaxation peak in the mechanical relaxation measurements. We find that the slow β-relaxation behavior can be tuned by modification of the chemical composition and fragility. The structural origin of the slow β-relaxation and correlation between β-relaxation and α-relaxation in the MGs are also discussed. MGs with pronounced slow β-relaxation and tunable properties might provide a model system to investigate some long-standing issues in the glass field.