This paper is devoted to a new method which allows to compute the convex envelope of a given function, by an evolution equation and techniques of curve evolution. We study the problem in the context of viscosity solutions and we propose numerical algorithms, to convexify a function, in one and two dimensions. In the end, we validate the model by presenting various numerical results. Key words: convex envelope, curve evolution, viscosity solutions, nonlinear second order elliptic and parabolic PDE's, finite differences scheme.