The invention discloses a probabilistic neuron circuit, a topological structure of a probabilistic neural network and an application thereof. The probabilistic neuron circuit comprises an integral capacitor, a non-fixed threshold volatile device and a load resistor; One end of the fixed-threshold volatile device, and the other end of the volatile device is connected to one end of the load resistor. The network topology includes multiple input neuron circuits, multiple probabilistic neuron circuits, and lateral inhibitory neuron circuits; each probabilistic neuron circuit is used to perform a neural network based on its non-fixed excitation threshold and the electrical signals emitted by each input neuron circuit. Random excitation; the inhibitory neuron circuit is used to inhibit the excitation of other subsequent probabilistic neuron circuits when receiving the signals excited by the first n probability neuron circuits. The invention introduces a non-fixed threshold volatile device into the neuron circuit, which greatly expands the application of the neuron circuit, especially can be used to solve non-deterministic problems, and has reliable solution results.