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Abstract Inspired by recent measurement of possible fully charmed tetraquarks in LHCb Collaboration, we investigate the mass spectra of fully heavy tetraquarks $$QQ {\bar{Q}} {\bar{Q}}$$ Q Q Q ¯ Q ¯ in an extended relativized quark model. Our estimations indicate that the broad structure around 6.4 GeV should contain one or more ground states for $$cc {\bar{c}} {\bar{c}}$$ c c c ¯ c ¯ tetraquarks, while the narrow structure near 6.9 GeV can be categorized as the first radial excitation of $$cc {\bar{c}} {\bar{c}}$$ c c c ¯ c ¯ system. Moreover, with the wave functions of the tetraquarks and mesons, the strong decays of tetraquarks into heavy quarkonium pair are qualitatively discussed, which can be further checked by the LHCb and CMS Collaborations.