This paper presents a fast algorithm based on the hysteretic transiently chaotic neural network (HTCNN) model for solving optimization problems. By using hysteretic activation function, HTCNN has higher ability of overcoming drawbacks that suffer from the local minimum. Meanwhile, in order to avoid oscillation and offer a considerable acceleration of converging to the optimal solution, a fast speed strategy is involved in HTCNN. Numerical simulation of a combinatorial optimization problem-assignment problem shows that HTCNN with fast speed strategy (FHTCNN) can overcome drawbacks that suffer from the local minimum and find the global optimal solutions quickly.