Abstract. A new model to simulate and predict the properties of a large ensemble of contrails as a function of given air traffic and meteorology is described. The model is designed for approximate prediction of contrail cirrus cover and analysis of contrail climate impact, e.g. within aviation system optimization processes. The model simulates the full contrail life-cycle. Contrail segments form between waypoints of individual aircraft tracks in sufficiently cold and humid air masses. The initial contrail properties depend on the aircraft. The advection and evolution of the contrails is followed with a Lagrangian Gaussian plume model. Mixing and bulk cloud processes are treated quasi analytically or with an effective numerical scheme. Contrails disappear when the bulk ice content is sublimating or precipitating. The model has been implemented in a "Contrail Cirrus Prediction Tool" (CoCiP). This paper describes the model assumptions, the equations for individual contrails, and the analysis-method for contrail-cirrus cover derived from the optical depth of the ensemble of contrails and background cirrus. The model has been applied for a case study and compared to the results of other models and in-situ contrail measurements. The simple model reproduces a considerable part of observed contrail properties. Mid-aged contrails provide the largest contributions to the product of optical depth and contrail width, important for climate impact.