Target tracking based on the space transformation model can usually be solved by dealing with the nonlinear least-square optimization problem. The geometric optimization algorithm based on the vector space has more limitation for high nonlinearities of the projective transformation. The mapping between a Lie group and its Lie algebra can make us to utilize the specific properties of the target tracking to propose a second-order minimization tracking method for the projective-based geometric warps within the intrinsic geometric optimization framework. In this approach, the Hessian matrix needs not to be calculated, so the computation complexity is reduced. Comparative experiments with the algorithm based on the vector space and the Gauss-Newton algorithm based on the Lie algebra parameterization validate the feasibility and high effectiveness of our method.