An analog memristor crossbar-based Lyapunov equation solver is proposed in this article. It is an extension of memristor crossbar linear equation solver, but taking into account of the regularity with Lyapunov equation in the organization of crossbar. Nonideal effects due to co-design with CMOS analog circuits are studied in detail. Verification using a Verilog-AMS tool is performed to justify that with proper scaling on the memristor conductance values and other circuit signals, the solution quality of Lyapunov matrix equation can be improved.