This study introduces a new Generalized Leaky Integrate-and-Fire (GLIF) neuron model with variable leaking resistor and bias current in order to reproduce accurately the membrane voltage dynamics of a biological neuron. The accuracy of this model is ensured by adjusting its parameters to the statistical properties of the Hodgkin-Huxley model outputs; while the speed is enhanced by introducing a Generalized Exponential Moving Average method that converts the parameterized kernel functions into pre-calculated lookup tables based on an analytic solution of the dynamic equations of the GLIF model.