Most brain models focus on associative memory or calculation capability, experimentally inaccessible using physiological methods. Here we present a model explaining a basic feature of electroencephalograms (EEG). Our model is based on an electrical network with threshold firing and plasticity of synapses that reproduces very robustly the measured exponent 0.8 of the medical EEG spectra, a solid evidence for self-organized criticality. Our result are also valid on small-world lattices. We propose that an universal scaling behaviour characterizes many physiological signal spectra for brain controlled activities.