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Much sensory-motor behavior develops through imitation, as during the learning of handwriting by children. Such complex sequential acts are broken down into distinct motor control synergies, or muscle groups, whose activities overlap in time to generate continuous, curved movements that obey an inverse relation between curvature and speed. How are such complex movements learned through attentive imitation? Novel movements may be made as a series of distinct segments, but a practiced movement can be made smoothly, with a continuous, often bell-shaped, velocity profile. How does learning of complex movements transform reactive imitation into predictive, automatic performance? A neural model is developed which suggests how parietal and motor cortical mechanisms, such as difference vector encoding, interact with adaptively timed, predictive cerebellar learning during movement imitation and predictive performance. To initiate movement, visual attention shifts along the shape to be imitated and generates vector movement using motor cortical cells. During such an imitative movement, cerebellar Purkinje cells with a spectrum of delayed response profiles sample and learn the changing directional information and, in turn, send that learned information back to the cortex and eventually to the muscle synergies involved. If the imitative movement deviates from an attentional focus around a shape to be imitated, the visual system shifts attention, and may make an eye movement, back to the shape, thereby providing corrective directional information to the arm movement system. This imitative movement cycle repeats until the cortico-cerebellar system can accurately drive the movement based on memory alone. A cortical working memory buffer transiently stores the cerebellar output and releases it at a variable rate, allowing speed scaling of learned movements which is limited by the rate of cerebellar memory readout. Movements can be learned at variable speeds if the density of the spectrum of delayed cellular responses in the cerebellum varies with speed. Learning at slower speeds facilitates learning at faster speeds. Size can be varied after learning while keeping the movement duration constant (isochrony). Context-effects arise from the overlap of cerebellar memory outputs. The model is used to simulate key psychophysical and neural data about learning to make curved movements, including a decrease in writing time as learning progresses; generation of unimodal, bell-shaped velocity profiles for each movement synergy; size and speed scaling with preservation of the letter shape and the shapes of the velocity profiles; an inverse relation between curvature and tangential velocity; and a Two-Thirds Power Law relation between angular velocity and curvature.