Non-centrosymmetric superconducting materials represent an exciting class of novel superconductors featuring a variety of unconventional properties, including mixed-parity pairing and very high upper critical fields. Here, we present a comprehensive study of TaIr₂B₂ (with T_c=5.1K), using a set of complementary experimental methods, including bulk- and surface-sensitive techniques. We provide evidence that this system is a two-band, yet it behaves as a single-gap superconductor with a strong coupling. The upper critical field of TaIr₂B₂ significantly exceeds the Pauli limit and exhibits a nearly linear temperature dependence down to the lowest temperatures. This behavior, rarely seen in superconductors, is discussed in terms of anti-symmetric spin–orbit interaction, two-band-, and strong-coupling effects, as well as disorder.