Abstract: In order to leverage the sparse characteristics of power line communication channel and improve the reliability of G3-PLC system communication, this paper proposes a sparsity adaptive variable step size forward-backward pursuit (SA-VSSFBP) algorithm based on the theory of compressed sensing (CS). This algorithm builds upon the forward-backward pursuit (FBP) algorithm and introduces the concept of variable step size with adaptivity. It employs a large step size in the initial iterations to reduce the number of iterations, and a small step size in the later iterations to obtain accurate estimates. Additionally, the atomic matching test is utilized for sparsity pre-estimation to ensure the approximation of the real sparsity, speed up the iteration speed and reduce the running time of the algorithm. The simulation results show that: compared with the traditional channel estimation method, the compressed sensing channel estimation method has superior performance; and compared with the orthogonal matching pursuit (OMP) and FBP compressed sensing channel estimation algorithms, the algorithm proposed in this paper is able to improve 24.14% and 47.2% of the efficiency of the algorithm in the case of guaranteeing that the accuracy is comparable to that of the FBP with the step size of 1.