To plan a global path in grid map, a hybrid two-dimensional path planning model based on frothing construction algorithm and local fast marching method is proposed. The proposed model consists of three steps. In first step, frothing construction algorithm is adopted to describe topology relationship of global passable regions in two-dimensional environment, and a grid topology map is obtained. The second step is path planning in topology map. Adopting generalized level-set algorithm, global shortest topology path can be obtained. In order to optimize the global path and real-time capability, global path replanning in grid map is proposed in third step. Local fast matching method is proposed by limiting effective region of cost potential function in global fast matching method. Quantitative analysis and comparisons prove that the proposed model is more suitable to the increasingly demanding path planning requirements than most of state-of-the-art algorithms.