The low-rank and sparse representation (LRSR) model and the deep learning (DL) model have already shown significant potential to detect anomalies in a hyperspectral image (HSI). However, the model-driven LRSR methods highly rely on manually configured regularization parameters, which causes subpar generalization capability. The data-driven DL methods lack interpretability due to their black-box nature. To boost the generalization capability and interpretability of the model, an LRSR-inspired interpretable network (LRSR-I2Net) is proposed in this article. First, the hyperspectral anomaly detection (HAD) task is modeled as an LRSR problem. Then, the iterative alternating direction method of multipliers (ADMM) algorithm for solving the LRSR problem is unrolled into an interpretable network (i.e., LRSR-I2Net), in which manually configured regularization parameters of the LRSR model are converted into trainable parameters of LRSR-I2Net. In this way, the generalization capability and interpretability of LRSR-I2Net can be guaranteed. To further mine the spatial information that LRSR methods ignored, the total variation regularization is introduced into the LRSR model as a piecewise smoothing constraint and designs an extended LRSR-I2Net with total variation (LRSR-I2Net-TV), which helps to maintain the spatial correlation of HSI and proves the scalability of the LRSR-I2Net framework. Experiments executed on multiple datasets show that LRSR-I2Net-TV performs well relative to eight comparison methods.