This paper proposes a new type of digital synchronous pulse mode neuron that employs a leakage integrator with additive random noise. Theoretical analysis and VHDL simulations verify the feasibility of the proposed neuron. The results show that the activation function of the neuron has small variance and that nonlinear activation function is invariable against the change of number of inputs. Also, synapse multiplier for the neuron is very simple and weight value is given in binary format.