Disclosed is a method and apparatus of operating a neural network. The neural network operation method includes receiving data for the neural network operation, verifying whether competition occurs between a first data traversal path corresponding to a first operation device and a second data traversal path corresponding to a second operation device, determining first operand data and second operand data from among the data using a result of the verifying and a priority between the first data traversal path and the second data traversal path, and performing the neural network operation based on the first operand data and the second operand data.