Multiband superconductivity and high critical current density in entropy-stabilized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Nb</mml:mi> <mml:mrow> <mml:mn>0.25</mml:mn> </mml:mrow> </mml:msub> <mml:msub

High-entropy alloy and medium-entropy alloy superconductors with significant intrinsic disorder are a fascinating class of superconductors to explore, both from a fundamental science perspective and for possible practical applications. Their combination of robust structural integrity, superior mechanical properties, and exceptional irradiation tolerance makes them promising candidates for use in aerospace, radiation-rich environments, and advanced superconducting technologies. Herein, we present a comprehensive theoretical and experimental investigation of the superconductivity of equiatomic entropy-stabilized ${\mathrm{Nb}}_{0.25}{\mathrm{Ta}}_{0.25}{\mathrm{Ti}}_{0.25}{\mathrm{Zr}}_{0.25}$. The material shows bulk superconductivity (transition temperature = 8 K) with a high upper critical field of 11.94 T. Interestingly, both the electronic band structure and specific heat data point toward unconventional multiband superconductivity. Our ab initio calculations reveal Dirac-like band crossings close to the Fermi level, with certain degeneracies persisting even in the presence of spin-orbit coupling, suggesting a possible interplay between topological electronic states and the observed unconventional superconductivity. Remarkably, the critical current density exceeds the benchmark of ${10}^{5}\phantom{\rule{0.28em}{0ex}}\mathrm{A}/{\mathrm{cm}}^{2}$, surpassing all previously reported as-cast entropy-stabilized superconductors. This high critical current density is likely attributed to strong flux pinning at the grain boundaries, facilitated by extreme intrinsic lattice distortion. Taken together, the demonstrated dynamical stability, excellent metallicity, potential to host unconventional superconductivity, and exceptionally high critical current density highlight the potential of entropy-stabilized alloys as a platform for exploring the confluence of disorder, topology, and unconventional superconductivity.