An　iterative　learning　control　(ILC)　algorithm　via　Taylor　series　is　presented　to　address　the　trajectory　tracking　of　a　class　of　linear　time-varying　systems　with　uncertain　exogenous　disturbance.　The　method　parameterizes　a　linear　time-varying　system　with　disturbance　by　using　Taylor　series　expansion.　Then,　an　approximated　model　for　the　system　is　deduced　by　employing　the　differential　relations　of　Taylor　series.　Based　on　the　model,　the　Taylor　series　coefficients　of　control　function　are　adjusted　by　an　iterative　learning　law　and　the　learning　gain　matrix　is　designed　via　LMI　optimization.　The　proposed　algorithm　can　use　the　error　signals　to　update　the　control　variable　even　when　the　systems　do　not　satisfy　regularity　nor　passivity.　Simulation　results　show　the　effectiveness　of　the　method.