The nonisothermal crystallization kinetics, fragility, and thermodynamics of Ti20Zr20Cu20Ni20Be20 high entropy bulk metallic glass (HE-BMG) have been investigated by differential scanning calorimetry. The activation energies for the glass transition and crystallization events were determined by Kissinger and Ozawa methods. The value of local Avrami exponent is less than 1.5 in most cases for all the three crystallization events, indicating that the major crystallization mechanism is diffusion-controlled growth of pre-existing nuclei. The local activation energy is stable during the whole crystallization process and this further confirms that the crystallization occurs through a single mechanism. Ti20Zr20Cu20Ni20Be20 alloy can be classified into “strong glass formers” according to the estimated fragility index and also shows a relatively low value of Gibbs free energy difference. However, compared with Zr41.2Ti13.8Cu12.5Ni10Be22.5 BMG, the glass-forming ability of Ti20Zr20Cu20Ni20Be20 HE-BMG is much lower and the related reasons have been discussed.