The thermal stability and non-isothermal crystallization of a new bulkamorphous high-entropy (HE-BMG) equiatomic GdYScAlCo alloy were studied by differential scanning calorimetry (DSC). The alloy shows a four-stage crystallization process. The kinetic parameters (activation energy (Eα)), the pre-exponential factor (logA) and glass-forming ability indicators (kinetic fragility index, characteristic temperatures) for the GdYScAlCo alloy were obtained. The Eα values obtained by isoconversional methods indicate a nonlinear Arrhenian behaviour and a complex process. The Avrami equation modification proposed by Jeziorny and the multivariate nonlinear regression method were applied on the nonisothermal crystallization. In the case of primary crystallization of the amorphous GdYScAlCo alloy under nonisothermal conditions, the kinetics of the nucleation process is best described by an autocatalytic reaction.