Centre-surround inhibition--the suppression of activity of neighbouring cells by a central group of neurons--is a fundamental mechanism that increases contrast in patterned sensory processing. The initial stage of neural processing in olfaction occurs in olfactory bulb glomeruli, but evidence for functional interactions between glomeruli is fragmentary. Here we show that the so-called 'short axon' cells, contrary to their name, send interglomerular axons over long distances to form excitatory synapses with inhibitory periglomerular neurons up to 20-30 glomeruli away. Interglomerular excitation of these periglomerular cells potently inhibits mitral cells and forms an on-centre, off-surround circuit. This interglomerular centre-surround inhibitory network, along with the well-established mitral-granule-mitral inhibitory circuit, forms a serial, two-stage inhibitory circuit that could enhance spatiotemporal responses to odours.