Abstract In this paper, we study the exponential growth of ⁎-graded identities of a finite dimensional ⁎-superalgebra A over a field F of characteristic zero. If a ⁎-superalgebra A satisfies a non-trivial identity, then the sequence { c n gri ( A ) } n ≥ 1 of ⁎-graded codimensions of A is exponentially bounded and so we study the ⁎-graded exponent exp gri ( A ) : = lim n → ∞ ⁡ c n gri ( A ) n of A . We show that exp gri ( A ) = dim F ⁡ ( A ) if and only if A is a simple ⁎-superalgebra and F is the symmetric even center of A . Also, we characterize the finite dimensional ⁎-superalgebras such that exp gri ( A ) ≤ 1 by the exclusion of four ⁎-superalgebras from var gri ( A ) and construct eleven ⁎-superalgebras E i , i = 1 , … , 11 , with the following property: exp gri ( A ) > 2 if and only if E i ∈ var gri ( A ) , for some i ∈ { 1 , … , 11 } . As a consequence, we characterize the finite dimensional ⁎-superalgebras A such that exp gri ( A ) = 2 .