  We report a study of the magnetic and electronic properties of the
non-centrosymmetric half-Heusler antiferromagnet HoPdBi ($T_N = 2.0$ K).
Magnetotransport measurements show HoPdBi has a semimetallic behaviour with a
carrier concentration $n=3.7 \times 10^{18}$ cm$^{-3}$ extracted from the
Shubnikov-de Haas effect. The magnetic phase diagram in the field-temperature
plane has been determined by transport, magnetization and thermal expansion
measurements: magnetic order is suppressed at $B_M\sim 3.6$ T for $T
\rightarrow 0$. Superconductivity with $T_c \sim 1.9$ K is found in the
antiferromagnetic phase. Ac-susceptibility measurements provide solid evidence
for bulk superconductivity below $T_c = 0.75$ K with a screening signal close
to a volume fraction of 100 %. The upper critical field shows an unusual linear
temperature variation with $B_{c2}(T \rightarrow 0) = 1.1$ T. We also report
electronic structure calculations that classify HoPdBi as a new topological
semimetal, with a non-trivial band inversion of 0.25 eV.
