This paper presents a new scheduling approach for high-level synthesis based on a deterministic modified Hopfield model. Our model uses a four dimensional neural network architecture to schedule the operations of a data flow graph (DFG) and maps them to specific functional units. Neural Network-based Scheduling (NNS) is achieved by formulating the scheduling problem in terms of an energy function and by using the motion equation corresponding to the variation of energy. The algorithm searches the scheduling space in parallel and finds the optimal schedule. The main contribution of this work is an efficient parallel scheduling algorithm under time and resource constraints appropriate for implementing on a parallel machine. The algorithm is based on moves in the scheduling space, which correspond to moves towards the equilibrium point (lowest energy state) in the dynamic system space. Neurons' motion equation is the core of this guided movement mechanism and guarantees that the state of the system always converges to the lowest energy state.