The Dirac semimetal PdTe2 was recently reported to be a type-I superconductor (Tc =1.64 K, µ0Hc(0) = 13.6 mT) with unusual superconductivity of the surface sheath. We here report a high-pressure study, p ≤ 2.5 GPa, of the superconducting phase diagram extracted from acsusceptibility and transport measurements on single crystalline samples. Tc(p) shows a pronounced non-monotonous variation with a maximum Tc =1.91 K around 0.91 GPa, followed by a gradual decrease to 1.27 K at 2.5 GPa. The critical field of bulk superconductivity in the limit T → 0, Hc(0, p), follows a similar trend and consequently the Hc(T, p)-curves under pressure collapse on a single curve: Hc(T, p) = Hc(0, p)[1 − (T /Tc(p)) 2 ]. Surface superconductivity is robust under pressure as demonstrated by the large superconducting screening signal that persists for applied dc-fields Ha > Hc. Surprisingly, for p ≥ 1.41 GPa the superconducting transition temperature at the surface T S c is larger than Tc of the bulk. Therefore surface superconductivity may possibly have a non-trivial nature and is connected to the topological surface states detected by ARPES. We compare the measured pressure variation of Tc with recent results from band structure calculations and discuss the importance of a Van Hove singularity.