Quasi-finite highest weight modules over W super(N) sub([)infinity]

In this paper, we classify the irreducible quasi-finite highest weight modules of the Lie subalgebras W super(N) sub([)infinity] ,pof the Lie algebra of matrix differential operators on the circle. We also realize the W super(N) sub([)infinity] modules in terms of the representation theory of the complex Lie algebra g[scriptl] super([infinity])[m] sub([infinity]) of infinite matrices with a finite number of nonzero diagonals with entries in the algebra of truncated polynomials.