The phase selection mechanism and eutectic growth kinetics of Nb_81.7Si_17.3Hf alloy are investigated by electrostatic levitation technique. The maximum undercooling of this alloy reaches 404 K (0.19T_L). By analyzing the cooling curves, its hypercooling limit is obtained to be 527 K (0.24T_L). A critical undercooling of 194 K is determined for the transition of solidification path. Below this undercooling threshold, (Nb) phase firstly nucleates and grows into primary dendrites, resulting in the enrichment of Si and Hf in the residual melt, which is conducive to the formation of the (Nb)+αNb₅Si₃ eutectics. Therefore, (Nb)+αNb₅Si₃ lamellar eutectics form in interdendritic space. With the increase of undercooling, the growth velocity of primary (Nb) dendritic follows a power function, while the eutectic growth velocity increases slowly. The maximum values of (Nb) dendritic reaches 89.4 mm/s. A modified LKT/BCT model is used to calculate the growth velocity of (Nb) dendrites. The results are in good agreement with the experimental values, indicating that after the LKT model is modified slightly, it can be used to describe the rapid dendrite growth behavior of the (Nb) phase in the Nb_81.7Si_17.3Hf alloy melt. Meanwhile, the lamellar spacing of (Nb)+αNb₅Si₃ eutectics notably decreases to 360 nm at 194 K undercooling. Above the critical threshold, the primary (Nb) dendrites disappear, whereas (Nb) phase and Nb₃Si phase nucleate independently in the undercooled liquid and grow into anomalous eutectics. The growth velocity of anomalous eutectic exhibits a power function relationship with the increase of undercooling, with a maximum value of 115.9 mm/s. The interphase spacing of (Nb)+Nb₃Si anomalous eutectics is larger than that of (Nb)+αNb₅Si₃ lamellar eutectics. Owing to the formation of nanosized eutectics and the increase of volume fraction of (Nb) phase, the alloy fracture toughness at 194 K reaches 21.9 MPa·m^1/2, which is 3.4 times as large as that under small undercooling condition.