An　iterative　learning　control　(ILC)　algorithm　based　on　Shifted　Legendre　orthogonal　polynomials　is　presented　to　address　the　terminal　control　problem　of　a　linear　time-varying　systems.　By　employing　the　orthogonality　relations　and　boundary　values　of　Shifted　Legendre　polynomials,　the　differential　equations　are　converted　into　a　set　of　linear　algebraic　equations,　and　the　control　problem　is　reduced　to　finding　the　Shifted　Legendre　polynomials　coefficients　of　control　variable.　So　the　method　avoids　computing　the　state　transfer　matrix,　and　the　coefficients　are　determined　iteratively　by　a　high　order　learning　algorithm.　Simulation　results　show　the　effectiveness　of　the　proposed　iterative　learning　scheme.