Rapid growth of amyloid fibrils via a seeded conformational conversion of monomers is a critical step of fibrillization and important for disease transmission and progression. Amyloid fibrils often display diverse morphologies with distinct populations, and yet the molecular mechanisms of fibril elongation and their corresponding morphological dependence remain poorly understood. Here, we computationally investigated the single-molecular growth of two experimentally resolved human islet amyloid polypeptide fibrils of different morphologies. In both cases, the incorporation of monomers into preformed fibrils was observed. The conformational conversion dynamics was characterized by a small number of fibril growth intermediates. Fibril morphology affected monomer binding at fibril elongation and lateral surfaces as well as the seeded conformational conversion dynamics at the fibril ends, resulting in different fibril elongation rates and populations. We also observed an asymmetric fibril growth as in our prior experiments, attributing to differences of two fibril ends in terms of their local surface curvatures and exposed hydrogen-bond donors and acceptors. Together, our mechanistic findings afforded a theoretical basis for delineating different amyloid strains-entailed divergent disease progression.