In this paper, a data-driven iterative learning control with neural network-based optimisation method for distributed parameter systems is presented to solve a class of problems caused by the imprecise mathematical model. The forward difference format is used to establish a linear relationship between input and output data, which is the only information available. However, this also leads to an unknown parameter matrix of the system. To overcome this problem, the radial basis function neural network is used to form a mapping relation from the desired output to the desired input, and the iterative learning algorithm of neural network weight is obtained by optimising the system performance indexes. Then, a detailed theoretical analysis based on composite energy function is given. Moreover, unlike traditional iterative learning control task tracking the whole trajectory, tracking time terminal is taken into account in this paper. Finally, simulation results show the feasibility of the theory.