Solving systems of linear equations is a fundamental problem in scientific computing, which has been extensively researched for decades. One of the most well-known solvers is Algebraic Multigrid (AMG), which is widely used in high performance computing due to its good scalability. But currently accelerating AMG relies on the traditional von Neumann architecture of storage and computation separation, which leads to a large data transmission overhead. In this work, we propose a ReRAM-based processing-in-memory (PIM) architecture named AmgR, which overcomes the limitations of the traditional von Neumann architecture for AMG acceleration.However, accelerating AMG on ReRAM is non-trivial, because (1) AMG has many computing kernels of various types; (2) there are irregular operations that cannot be directly performed using matrix-vector multiplication suitable for ReRAM, i.e., aggregation operation; (3) ReRAM has poor write endurance, and a lot of data during AMG acceleration needs to be rewritten into ReRAM, resulting in high write cost. To address these issues, firstly, we propose a flexible architecture, which can realize each kernel of AMG and is reused by many kernels to improve resource utilization. Secondly, we propose a dedicated unit to realize the aggregation operation. Finally, we present a new mapping strategy to greatly reduce the number of data handling and writes. The experimental results show that the performance of AmgR is improved by an average of one and two orders of magnitude compared to HYPRE on the CPU and AmgX on the GPU, respectively, while the energy consumption is reduced by an average of two and three orders of magnitude.