An　iterative　learning　control　algorithm　based　on　shifted　Legendre　orthogonal　polynomials　is　proposed　to　address　the　terminal　control　problem　of　linear　time-varying　systems.　First,　the　method　parameterizes　a　linear　time-varying　system　by　using　shifted　Legendre　polynomials　approximation.　Then,　an　approximated　model　for　the　linear　time-varying　system　is　deduced　by　employing　the　orthogonality　relations　and　boundary　values　of　shifted　Legendre　polynomials.　Based　on　the　model,　the　shifted　Legendre　polynomials　coefficients　of　control　function　are　iteratively　adjusted　by　an　optimal　iterative　learning　law　derived.　The　algorithm　presented　can　avoid　solving　the　state　transfer　matrix　of　linear　time-varying　systems.　Simulation　results　illustrate　the　effectiveness　of　the　proposed　method.