A vehicle driving assist system has a controller configured to calculate a risk potential indicative of the degree of convergence between a host vehicle in which the system is installed and a preceding obstacle. Then, the controller performs a driver notification controlling operation that produces a driver notification stimulus based on the risk potential. Considering the acceleration of the preceding obstacle, the speed of the host vehicle, and the following distance between the host vehicle and the preceding obstacle, the controller calculates a threshold value for determining when to commence the control of the driver notification controlling operation.