This paper proposes adaptive estimation and control methods for vehicle semi-active suspension systems with magneto-rheological (MR) damper. To incorporate MR damper into the control design, a hyperbolic model is adopted to describe its dynamics, and then adaptive parameter estimation is firstly studied to estimate the unknown parameters of the hyperbolic model. This estimation method requires the measured piston variable and damper force, and can be taken as a further extension of our recently proposed parameter estimation error based algorithms. Moreover, an adaptive control is designed to stabilize the vertical vehicle displacement to improve the ride comfort, where an alternative leakage term is introduced in the adaptive law to guarantee simultaneously the precise estimation of several essential parameters (e.g. mass of vehicle body and MR damper parameters) and the control convergence. The closed-loop system stability is proved and relevant suspension performance requirements are analyzed. Finally, simulations based on a quarter-car model are provided to validate the proposed method.