Indecomposable representations of Lie superalgebras are studied on quotient spaces of the universal enveloping algebra of the Heisenberg-Weyl superalgebra (b⁺_i,b_i,f⁺_u,e) by boson-fermion realisation. These representations are constructed from certain types of indecomposable representations of the Heisenberg-Weyl superalgebra and induce usual irreducible representations on invariant subspaces of a quotient space. As a physically significant example, the explicit form of the boson-fermion realisation of indecomposable representations of the classical Lie superalgebra SU(2/1) are obtained and discussed.