High-entropy alloys (HEAs) are at the focus of current research for their diverse properties, including superconductivity and structural polymorphism. However, the polymorphic transition has been observed only in nonsuperconducting HEAs and mostly under high pressure. Here we report the discovery of superconductivity and temperature-driven polymorphism in the (V$_{0.5}$Nb$_{0.5}$)$_{3-x}$Mo$_{x}$Al$_{0.5}$Ga$_{0.5}$ (0.2 $leq$ $x$ $leq$ 1.4) HEAs. It is found that the as-cast HEA is of a single body-centered cubic (bcc) structure for $x$ = 0.2 and a mixture of the bcc and A15 structures for higher $x$ values. Upon annealing, the bcc structure undergoes a polymorphic transformation to the A15 one and all HEAs exhibits bulk superconductivity. For $x$ = 0.2, whereas the bcc polymorph is not superconducting down to 1.8 K, the A15 polymorph has a superconducting transition temperature $T_{rm c}$ of 10.2 K and an estimated zero-temperature upper critical field $B_{rm c2}$(0) of 20.1 T, both of which are the highest among HEA superconductors. With increasing Mo content $x$, both $T_{rm c}$ and $B_{rm c2}$(0) of the A15-type HEAs decrease, yet the large ratio of $B_{rm c2}$(0)/$T_{rm c}$ signifies a disorder-induced enhancement of the upper critical field over a wide $x$ range. The decrease in $T_{rm c}$ is attributed to the decrease in both the electronic specific-heat coefficient and electron-phonon coupling strength. Furthermore, the valence electron count dependence of $T_{rm c}$, which is different from both the binary A15 and other structurally different HEA superconductors, suggests that $T_{rm c}$ may be increased further by reducing the number of valence electrons. Our results not only uncover HEA superconductors of a new structural type, but also provide the first example of polymorphism dependent superconductivity in HEAs.
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