Compressive sensing (CS) has been widely applied in signal and image processing fields. Traditional CS reconstruction algorithms have a complete theoretical foundation but suffer from the high computational complexity, while fashionable deep network-based methods can achieve high-accuracy reconstruction of CS but are short of interpretability. These facts motivate us to develop a deep unfolding network named the penalty-based independent parameters optimization network (PIPO-Net) to combine the merits of the above mentioned two kinds of CS methods. Each module of PIPO-Net can be viewed separately as an optimization problem with respective penalty function. The main characteristic of PIPO-Net is that, in each round of training, the learnable parameters in one module are updated independently from those of other modules. This makes the network more flexible to find the optimal solutions of the corresponding problems. Moreover, the mean-subtraction sampling and the high-frequency complementary blocks are developed to improve the performance of PIPO-Net. Experiments on reconstructing CS images demonstrate the effectiveness of the proposed PIPO-Net.