A longitudinal slope brake model was established for the radius calculation of vertical curve of free-way through analyzing the dynamics of brake-running of vehicles running on the longitudinal slope road section. To satisfy the requirement of sight distance, a relation model was established for the attachment coefficient and the convex vertical curve radius. Using MATLAB simulation technique, the convex vertical curve radius at different attachment conditions was calculated accurately and a three-dimensional figure was drawn to describe the relation between the adhesive coefficient, the driving velocity and the radius of vertical curve. The correlation between the convex vertical curve radius and the adhesive coefficient was further analyzed and compared with National Technical Standards. The suggested radius of vertical curve was then put forward to provide a theoretical platform for the security design of the convex vertical curve.