The architecture of parallel fiber axons contacting cerebellar Purkinje neurons retains spatial information over long distances. Parallel fiber synapses can trigger local dendritic calcium spikes, but whether and how this calcium signal leads to plastic changes that decode the parallel fiber input organization is unknown. By combining voltage and calcium imaging, we show that calcium signals, elicited by parallel fiber stimulation and mediated by voltage-gated calcium channels, increase non-linearly during high-frequency bursts of electrically constant calcium spikes, because they locally and transiently saturate the endogenous buffer. We demonstrate that these non-linear calcium signals, independently of NMDA or metabotropic glutamate receptor activation, can induce parallel fiber long-term potentiation. Two-photon imaging in coronal slices revealed that calcium signals inducing long-term potentiation can be observed by stimulating either the parallel fiber or the ascending fiber pathway. We propose that local dendritic calcium spikes, evoked by synaptic potentials, provide a unique mechanism to spatially decode parallel fiber signals into cerebellar circuitry changes.