With the development of the controllable suspension systems, the mono-tube hydraulic adjustable damper has attracted great public attention with the advantages such as good heat dissipation, less power, fast response, durable, reliable, and simple structure. However, the unknown regulating mechanism modeling impedes the practical application of the mono-tube hydraulic adjustable damper. To model the regulating mechanism, this paper analytically studies the behavior of the mono-tube hydraulic adjustable damper via developing an analytical model and thermal effect equations for the use of engineering design. Then, the mono-tube hydraulic adjustable damper is tested in an integral shock absorber testing system to verify the accuracy of model and equations. On the basis of the verified analytical model and thermal effect equations, a compensation system with gray neural network algorithm is originally designed to model the regulating mechanism of the mono-tube hydraulic adjustable damper, thus achieving the desired damping force adaptively and accurately at various working conditions by obtaining the required rotary angle of the adjustment rod. The simulation results and experimental results show that the characteristic analyses of mono-tube hydraulic adjustable damper are reliable. Meanwhile, the simulation results of the gray neural network algorithm also indicate that the proposed compensation system can provide an exact regulating mechanism model for the mono-tube hydraulic adjustable damper and the proposed gray neural network algorithm is superior to the traditional neural network algorithm.