Skin background colour is a very important quality aspect in the grading of ‘Jonagold’ apples, with consumers usually preferring fruit with a green background colour. However, apple handlers are usually faced with large fruit-to-fruit variability of background colour within a population of fruit. In this study, a stochastic modelling approach is used to describe how the initial fruit-to-fruit variability in the background colour of ‘Jonagold’ apples present at harvest, propagates throughout the postharvest chain. Two hundred fruit were harvested and stored at 1 or 4°C, under different controlled atmosphere (CA) conditions for six months. The fruit were taken out of storage every two months, and the background colour and the ethylene production of individual fruit were measured. At the end of the six months storage, the fruit were placed in shelf life conditions for 15 days, during which skin background colour and ethylene production were measured every five days. A mathematical model was developed to describe the postharvest loss of the skin greenness of apples during CA storage, by assuming that the loss is principally due to chlorophyll breakdown, the rate of which is dependent on the endogenous ethylene concentration within the fruit. The stochastic model parameters in the model were identified, and by treating these parameters as fruit-specific parameters, the model could describe more than 93% of the data for the individual fruit. By considering these fruit-specific parameters as stochastic parameters, the Monte Carlo method was used to describe the propagation of the fruit-to-fruit variability of the background colour of ‘Jonagold’ apples within a population. The model developed in this study can be used to predict how the initial fruit-to-fruit variability within a batch of apple will propagate throughout the postharvest chain.