  We report our point-contact spectroscopy (PCS) study on the superconducting
state of the type-II Dirac semimetal PdTe$_2$ with a superconducting transition
temperature $T\rm_c \sim$ 1.65 K. Both mechanical- and soft- PCS differential
conductance curves at 0.3 K show a consistent double-peak structure and they
can be perfectly fitted by a single s-wave gap based on the
Blonder-Tinkham-Klapwijk model. The gap follows a typical
Bardeen-Cooper-Schrieffer temperature behavior, yielding $\Delta_0 \sim$ 0.29
meV and 2$\Delta_0$/$k\rm_{B}$$T\rm_{c}$ = 4.15 in the strong coupling regime.
A sudden suppression of the superconducting gap in magnetic field around
$H{\rm_{c1}}$ $\sim$ 130 Oe is observed for most point-contacts on PdTe$_2$,
characteristic of a first-order transition for type-I superconductor in field.
However, for other contacts, a smooth evolution of the PCS conductance persists
up to $H{\rm_{c2}}$ $\sim$ 600 Oe, signaling a local type-II superconductivity.
The observed admixture of type-I and type-II superconductivity can possibly
arise from an inhomogeneous electron mean free path on the surface of PdTe$_2$
due to its topological surface states.
