In land plants, the cell plate partitions the daughter cells at cytokinesis. The cell plate initially forms between daughter nuclei and expands centrifugally until reaching the plasma membrane. The centrifugal development of the cell plate is driven by the centrifugal expansion of the phragmoplast microtubule array, but the molecular mechanism underlying this expansion is unknown. Here, we show that the phragmoplast array comprises stable microtubule bundles and dynamic microtubules. We find that the dynamic microtubules are nucleated by γ-tubulin on stable bundles. The dynamic microtubules elongate at the plus ends and form new bundles preferentially at the leading edge of the phragmoplast. At the same time, they are moved away from the cell plate, maintaining a restricted distribution of minus ends. We propose that cycles of attachment of γ-tubulin complexes onto the microtubule bundles, microtubule nucleation and bundling, accompanied by minus-end-directed motility, drive the centrifugal development of the phragmoplast.