  Combination of different nontrivial topological states in a single material
is capable of realizing multiple functionalities and exotic physics, but such
materials are still very sparse. We report herein the results of
magnetotransport measurements and ab initio calculations on single crystalline
CaAl2Si2 semimetal. The transport properties could be well understood in
connection with the two-band model, agreeing well with the theoretical
calculations indicating four main sheets of Fermi surface consisting of three
hole pockets centered at the {\Gamma} point and one electron pocket centered at
the M point in the Brillouin zone. The single fundamental frequency imposed in
the quantum oscillations of magnetoresistance corresponds to the electron Fermi
pocket. Without spin-orbit coupling (SOC), the ab initio calculations suggest
CaAl2Si2 as a system hosting a topological nodal-line setting around the
{\Gamma} point in the Brillouin zone close to the Fermi level. Once including
the SOC, the fragile nodal-line will be gapped and a pair of Dirac points
emerge along the high symmetric {\Gamma}-A direction, which is about 1.22 eV
below the Fermi level. The SOC can also induce a topological insulator state
along the {\Gamma}-A direction with a gap of about 3 meV. The results
demonstrate CaAl2Si2 as an excellent platform for the study of novel
topological physics with multiple topological states.
