The formation of functional neural networks requires precise regulation of the growth and branching of the terminal arbors of axons, processes known to be influenced by early network electrical activity. Here we show that a rule of activity-based competition between neighbouring axons appears to govern the growth and branching of retinal ganglion cell (RGC) axon arbors in the developing optic tectum of zebrafish. Mosaic expression of an exogenous potassium channel or a dominant-negative SNARE protein was used to suppress electrical or neurosecretory activity in subsets of RGC axons. Imaging in vivo showed that these forms of activity suppression strongly inhibit both net growth and the formation of new branches by individually transfected RGC axon arbors. The inhibition is relieved when the activity of nearby 'competing' RGC axons is also suppressed. These results therefore identify a new form of activity-based competition rule that might be a key regulator of axon growth and branch initiation.