<p>Real-time knowledge of the tire–road friction coefficient is essential for various vehicle control systems, including antilock braking, vehicle stability control, and collision avoidance systems. This paper investigates a tire–road friction estimation method based on the brush tire model. In previous studies, a quintic equation has been derived to determine the tire grip margin, which is defined as the residual tire force divided by the product of the tire–road friction coefficient and the vertical tire load. In this paper, Brent’s method, a numerical root-finding approach, is used to determine the tire grip margin. The initial search interval for Brent’s method is established using two cubic approximating polynomials. Once the tire grip margin is obtained, it can be directly converted into the tire–road friction coefficient. Simulation results based on the Dugoff tire model demonstrate good agreement between the estimated and actual friction coefficients, as well as between the estimated and actual tire force usage.</p>