  By measuring the de Hass-van Alphen effect and calculating the electronic
band structure, we have investigated the bulk Fermi surface of the BaSn3
superconductor with a transition temperature of ~ 4.4 K. Striking de Haas-van
Alphen (dHvA) quantum oscillations are observed when the magnetic field B is
perpendicular to both (100) and (001) planes. Our analysis unveiled nontrivial
Berry phase imposed in the quantum oscillations when B is perpendicular to
(100), with two fundamental frequencies at 31.5 T and 306.7 T, which likely
arise from two corresponding hole pockets of the bands forming a type-II Dirac
point. The results are supported by the ab initio calculations indicating a
type-II Dirac point setting and tilting along the high symmetric K-H line of
the Brillouin zone, about 0.13 eV above the Fermi level. Moreover, the
calculations also revealed other two type-I Dirac points on the high symmetric
{\Gamma}-A direction, but slightly far below the Fermi level. The results
demonstrate BaSn3 as an excellent platform for the study of not only exotic
properties of different types of Dirac fermions in a single material, but also
the interplay between nontrivial topological states and superconductivity.
