Observations of AGN show that they generally possess a high metallicity, varying from solar to supersolar metallicities. This is the case since AGN are usually found in massive, bulge-dominated galaxies that have converted most of their gas into stars by the present epoch. Since AGN metallicity is strongly correlated with stellar mass, low-metallicity AGN are expected to be in low-mass dwarf galaxies. However, until now, searches in low-mass galaxies have only turned up AGN with metallicities around half that of typical AGN, i.e. with solar or slightly subsolar values. We report the discovery of four low-metallicity dwarf galaxies in the Data Release 6 of the Sloan Digital Sky survey, with 12 + log O/H in the range 7.4–8.0, and that appear to harbor an AGN. In the course of a long-range program to search for extremely metal-deficient emission-line dwarf galaxies, we have come across four galaxies with very unusual spectra: the strong permitted emission lines, mainly the Hα line, show very prominent broad components, with full widths at zero intensity corresponding to velocities varying between 2200 and 3500 km s−1, and extraordinarily large broad Hα luminosities, varying from 3×1041 to 2×1042 erg s−1. The Balmer lines show a very steep decrement, suggesting collisional excitation and that the broad emission comes from very dense gas (Ne ≫ 104 cm−3). Only the presence of an accretion disk around an intermediate-mass black hole in the dwarf galaxies appears to account for these properties.