Iterative learning control problem is studied for a class of discrete nonlinear partial difference systems where the trial lengths vary randomly in this paper. The considered systems are composed of parabolic partial difference equations. Firstly， for the trial lengths vary randomly in systems， a stochastic variable satisfying Bernoulli distribution is introduced. Then， according to the properties of partial difference systems and P-type distributed update schemes， iterative learning controller is designed. Through rigorous theoretical analysis， the convergence sufficient condition of output error under λ norm and contractive mapping principle is established to ensure the convergence of tracking error in the sense of norm. The convergence speed of the algorithm is faster than the classical iterative learning algorithm. Finally， the effectiveness of the algorithm is verified by the numerical simulation.