Conventional long-horizon finite-control-set model predictive control (FCS-MPC) for power electronics has two main real-time implementation problems, 1) calculation burden and latency; 2) high hardware resource requirements on real-time platforms such as FPGA. To solve these problems, machine learning models have been proposed using model predictive control results as offline training data to train an artificial neural network (ANN), which will be implemented in the real-time controller instead of the original model predictive control model. In this way, the ANN reduces the online calculation burden and the hardware resource requirements. In this article, an FPGA-based 1-D convolution neural network (CNN) for long-horizon FCS-MPC is proposed. To simplify the network model and reduce the hardware resources further, model compression techniques of pruning, fine-tuning, and quantization are implemented. The proposed model is verified using a parallel hybrid converter as a case study converter, with performance and hardware resource requirements compared to conventional FCS-MPC and multilayer perceptron (MLP) models. The results show that the proposed compressed CNN model can reduce FPGA DSP resource requirements by 75% compared to an FCS-MPC model and an MLP model, while also achieving comparable or superior performance.