In frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems, downlink channel state information (CSI) needs to be sent back to the base station (BS) by the users, which causes prohibitive feedback over-head. In this paper, we propose a lightweight and flexible deep learning-based CSI feedback approach by capitalizing on deep equilibrium models. Different from existing deep learning-based methods that stack multiple explicit layers, we propose an implicit equilibrium block to mimic the behavior of an infinite-depth neural network. In particular, the implicit equilibrium block is defined by a fixed-point iteration and the trainable parameters in different iterations are shared, which results in a lightweight model. Furthermore, the number of forward iterations can be adjusted according to users’ computation capability, enabling a flexible accuracy-efficiency trade-off. Simulation results will show that the proposed design achieves a comparable performance as the benchmarks but with much-reduced complexity and permits an accuracy-efficiency trade-off at runtime.