A batch process can be viewed as a two-dimensional (2D) system with dynamics in both time and batch directions. To tackle these 2D dynamics, many control algorithms have been proposed by combining iterative learning control (TLC) with high-performance continuous control algorithms under a 2D framework. However, these algorithms require large computational load and memory, which are often demanding for the software and hardware of the controllers in several fast batch processes. In this paper, a 2D predictive functional control algorithm that combines ILC with predictive functional control (PFC) is proposed. Owing to the compactness and effectiveness of PFC, the proposed control algorithm can reduce the required computational load and memory. Other than the general form of the control law, two concise and practical forms are provided as well. The proposed control scheme is tested through simulations and implementation in an injection molding process, which is a typical fast batch process. Results confirm the good performance of the proposed control algorithm.