Point projection on an implicit surface is essential for the geometric modeling and graphics applications of it. This paper presents a method for computing the principle curvatures and principle directions of an implicit surface. Using the principle curvatures and principle directions, we construct a torus patch to approximate the implicit surface locally. The torus patch is second order osculating to the implicit surface. By taking advantage of the approximation torus patch, this paper develops a second order geometric iterative algorithm for point projection on the implicit surface. Experiments illustrate the efficiency and less dependency on initial values of our algorithm.