  N-fold supersymmetry is an extension of the ordinary supersymmetry in
one-dimensional quantum mechanics. One of its major property is
quasi-solvability, which means that energy eigenvalues can be obtained for a
portion of the spectra. We show that recently found Type A N-fold supersymmetry
can be constructed by using sl(2) algebra, which provides a basis for the
quasi-solvability. By this construction we find a condition for the Type A
N-fold supersymmetry, which is less restrictive than the condition known
previously. Several explicitly known models are also examined in the light of
this construction.
