In this paper a new model approach for describing aeolian sediment transport in supply limited situations is presented. It is aimed to formulate a model which can handle both supply limited as transport limited conditions. The model consists of a 1D linear advection model where Bagnold type 3rd power sediment transport formulations are used to calculate transport potentials. Supply limitations are implemented in the model by evaluating if there is enough erodible sediment to reach the transport potential of the wind. To illustrate the capabilities of the model, three test cases are presented. It is found that the model is capable of describing aeolian sediment transport rates which are dependent on both wind speed and supply magnitude. Also fetch effects due to various causes can be reproduced by the model. The model is used to generate a time series of sediment transport and wind velocities and it is found that, in supply limited systems, aeolian sediment transport can be estimated using a linear model with respect to wind speed. This linear formulation is an alternative to traditional third power models which are often fitted to explain measured data. The linear model is used to fit previously collected field data. The model can be used to analyse field data where it is suggested that the model can provide a tool for estimating the variability of the supply magnitude. After calibration the model could be used as a predictive tool for aeolian sediment transport rates. Further validation of the principle is needed.