Combustion noise may become an important noise source for lean-burn gas turbine engines, and this noise is usually associated with highly unsteady flames. This work aims to compute the broadband combustion noise spectrum for a realistic aeroengine combustor, and to compare with available measured noise data on a demonstrator aeroengine. A low-order linear network model is applied to a demonstrator engine combustor to obtain the transfer function that relates to unsteadiness in the rate of heat release, acoustic, entropic and vortical fluctuations. A spectral model is used for the heat release rate fluctuation, which is the source of the noise. The mean flow of the aeroengine combustor required as input data to this spectral model is obtained from RANS simulations. The computed acoustic field for a low-medium power setting indicates that the models used in this study capture the main characteristics of the broadband spectral shape of combustion noise. Reasonable agreement with the measured spectral level is achieved.