Metallic glasses are metastable and their thermal stability is critical for practical applications, particularly at elevated temperatures. The conventional bulk metallic glasses (BMGs), though exhibiting high glass-forming ability (GFA), crystallize quickly when being heated to a temperature higher than their glass transition temperature. This problem may potentially be alleviated due to the recent developments of high-entropy (or multi-principle-element) bulk metallic glasses (HE-BMGs). In this work, we demonstrate that typical HE-BMGs, i.e., ZrTiHfCuNiBe and ZrTiCuNiBe, have higher kinetic stability, as compared with the benchmark glass Vitreoy1 (Zr41.2Ti13.8Cu12.5Ni10Be22.5) with a similar chemical composition. The measured activation energy for glass transition and crystallization of the HE-BMGs is nearly twice that of Vitreloy 1. Moreover, the sluggish crystallization region ΔTpl-pf, defined as the temperature span between the last exothermic crystallization peak temperature Tpl and the first crystallization exothermic peak temperature Tpf, of all the HE-BMGs is much wider than that of Vitreloy 1. In addition, high-resolution transmission electron microscopy characterization of the crystallized products at different temperatures and the continuous heating transformation diagram which is proposed to estimate the lifetime at any temperature below the melting point further confirm high thermal stability of the HE-BMGs. Surprisingly, all the HE-BMGs show a small fragility value, which contradicts with their low GFA, suggesting that the underlying diffusion mechanism in the liquid and the solid of HE-BMGs is different.