Self-assembly of proteins into amyloid aggregates displays a broad diversity of morphologies, both at the protofibrillar and final fibrillar species. These polymorphic species can coexist at fixed experimental conditions, and their relative abundance can be controlled by changing the solvent composition, or stirring the solution. However, the extent to which external conditions regulate the equilibrium of morphologically distinct species is still unknown. Here we investigate the nucleation of distinct fibril morphologies using computer simulations of a simplified model of an amyloid polypeptide. Counterintuitively, the energetically less favorable fibril morphologies nucleate more frequently than the morphologies of higher stability for models with low aggregation propensity. The free-energy profiles of the aggregation process indicate that the nucleation barrier determines the population fractions of different fibril morphologies, i.e., amyloid polymorphism is under kinetic control.