A high quality model of newborn EEG background can aid in the analysis of newborn EEG. This paper proposes an improvement to the current time-varying, power-law spectrum model for newborn EEG background by using a band-limited fractional Brownian process with time-varying Hurst exponent. This model provides a more detailed definition of newborn EEG background than current models. The advantages of using a fractional Brownian process is that development of features for analysing newborn EEG background is inherent in the model and simulation of continuous newborn EEG background with variable spectral characteristics is simplified. The model is validated by showing that a fractional Brownian process is indeed a suitable model for newborn EEG background using the statistical properties of a fractional Brownian process and a database of 1080 epochs of newborn EEG background. A newborn EEG background simulation algorithm, based on discrete time-varying FIR filtering, is then presented.