  In this paper, the notion of unitary vertex operator superalgebra is
introduced. It is proved that the vertex operator superalgebras associated to
the unitary highest weight representations for the Neveu-Schwarz Lie
superalgebra, Heisenberg superalgebras and to positive definite integral
lattices are unitary vertex operator superalgebras. The unitary structures are
then used to study the structures of vertex operator superalgebras, it is
proved that any unitary vertex operator superalgebra is a direct sum of strong
CFT type unitary simple vertex operator superalgebras. The classification of
unitary vertex operator superalgebras generated by the subspaces with conformal
weights less than or equal to $1$ is also considered.
