For a better learning transient along the iteration number direction. a PID-type iterative learning control algorithm is proposed for a class of delayed uncertain nonlinear systems which perform a given task repeatedly. The convergence conditions for the proposed high-order learning control have been established. The tracking error bound is proven to be a class-K function of the bounds of reinitialization errors, uncertainties and disturbances to the systems. It is also indicated that the time delays in the system stales do not play a significant role in the ILC convergence property. The effectiveness of the high-order ILC algorithm is demonstrated by simulation examples.