Abstract: A geometric iteration algorithm for projecting a point onto an implicit surface is presented.First,a special normal transversal at the initial point is constructed and a second-order Taylor's algorithm is used to trace the projections along the aforementioned normal transversal.A curvature based method for controlling iteration step is further proposed by projecting the given point onto the curvature circle of the normal transversal at the initial point.Finally gradient based method for correcting iteration errors is put forward.Simulations indicate that the proposed algorithm has good convergence,robustness and efficiency.