Large-Eddy simulation (LES) is performed to study pulsatile blood flow through a 3D model of arterial stenosis. The model is chosen as a simple channel with a biological type stenosis formed on the top wall. A sinusoidal non-additive type pulsation is assumed at the inlet of the model to generate time dependent oscillating flow in the channel and the Reynolds number of 1200, based on the channel height and the bulk velocity, is chosen in the simulations. We investigate in detail the transition-to-turbulent phenomena of the non-additive pulsatile blood flow downstream of the stenosis. Results show that the high level of flow recirculation associated with complex patterns of transient blood flow have a significant contribution to the generation of the turbulent fluctuations found in the post-stenosis region. The importance of using LES in modelling pulsatile blood flow is also assessed in the paper through the prediction of its sub-grid scale contributions. In addition, some important results of the flow physics are achieved from the simulations, these are presented in the paper in terms of blood flow velocity, pressure distribution, vortices, shear stress, turbulent fluctuations and energy spectra, along with their importance to the relevant medical pathophysiology.