  A pair of type-II Dirac cones in PdTe$_2$ was recently predicted by theories
and confirmed in experiments, making PdTe$_2$ the first material that processes
both superconductivity and type-II Dirac fermions. In this work, we study the
evolution of Dirac cones in PdTe$_2$ under hydrostatic pressure by the
first-principles calculations. Our results show that the pair of type-II Dirac
points disappears at 6.1 GPa. Interestingly, a new pair of type-I Dirac points
from the same two bands emerges at 4.7 GPa. Due to the distinctive band
structures compared with those of PtSe$_2$ and PtTe$_2$, the two types of Dirac
points can coexist in PdTe$_2$ under proper pressure (4.7-6.1 GPa). The
emergence of type-I Dirac cones and the disappearance of type-II Dirac ones are
attributed to the increase/decrease of the energy of the states at $\Gamma$ and
$A$ point, which have the anti-bonding/bonding characters of interlayer Te-Te
atoms. On the other hand, we find that the superconductivity of PdTe$_2$
slightly decreases with pressure. The pressure-induced different types of Dirac
cones combined with superconductivity may open a promising way to investigate
the complex interactions between Dirac fermions and superconducting
quasi-particles.
