In this paper, we present a new method, based on curve evolution, for the reconstruction of a 3D curve from two different projections. Given two views of some 3D curve, we propose to recover the curve minimizing energy functional. Following the work on geodesic active contour by Caselles et al. [2], we then transform the problem of minimizing the functional into a problem of geodesic computation in a Riemann space. The Euler-Lagrange equation of this new functional is derived and its associated PDE is solved using the level set formulation scheme. The motivation of this work is their application to the 3D reconstruction of the vessel from a biplane angiography.