Modeling driver steering behavior plays an ever-important role in nowadays automotive dynamics and control applications. Especially, understanding individuals' steering characteristics enables the advanced driver assistance systems (ADAS) to adapt to particular drivers, which provides enhanced protection while mitigating human-machine conflict. Driver-adaptive ADAS requires identifying the parameters inside a driver steering model in real-time to account for driving characteristics variations caused by weather, lighting, road, or driver physiological conditions. Usually, Recursive Least Squares (RLS) and Kalman Filter (KF) are employed to update the driver steering model parameters online. However, because of their asymptotical nature, the convergence speed of the identified parameters could be slow. In contrast, this paper adopts a purely algebraic perspective to identify parameters of a driver steering model, which can achieve parameter identification within a short period. To demonstrate the effectiveness of the proposed method, we first apply synthetic driver steering data from simulation to show its superior performance over an RLS identifier in identifying constant model parameters, including feedback steering gain, feedforward steering gain, preview time, and first-order neuromuscular lag. Then, we utilize real measurement data from human subject driving simulator experiments to illustrate how the time-varying feedback and feedforward steering gains can be updated online via the algebraic method.