Abstract: Over a field of characteristic p≥3,this paper determines the 0-th cohomology from Witt-type Modular Lie superalgebra W(2)to all restricted and non-restricted Kac modules K_S(λ).We show that the 0-th cohomology spaces of W(2)with coefficients in K_S(λ)is 1-dimensional if S=0, λ=(0,2),and the 0-th cohomology spaces of W(2)with coefficients in K_S(λ)is 0-dimensional if S≠0 or λ≠(0,2).

Key words: Witt-type modular Lie superalgebra, Kac module, cohomology