Visibility and average velocity are interrelated aspects that impact safety, traffic flow, environmental impact, driver well-being, and regulatory compliance in driving and transportation. Optimizing road safety and efficiency requires skillfully balancing these aspects. We developed a new car-following model to study the impact of visibility and average velocity information on traffic flow. The “headway-sensitivity” phase analysis reveals that the stable zone continues to grow as visibility decreases and more attention is paid to the average velocity information of the transportation ahead. The “kink-antikink” solution of the “mKdV equation”, related to the visibility and driver’s attention effects, is derived by nonlinear analysis. Numerical simulation is conducted to validate the theoretical findings. As visibility decreases, traffic flow becomes increasingly stable. Low visibility negatively impacts traffic flow because traffic current becomes down with less visibility, but if the driver gets more information about the number of vehicles ahead, then the stability increases with less visibility.