We systematically calculate the mass spectrum of higher excited fully charmed tetraquark $cc\overline{c}\overline{c}$ states including $S$-wave radial excitations and $P$-wave with a nonrelativistic quark model. The model is composed vector one-gluon-exchange scalar linear confinement interaction parameters determined by charmonium spectrum. In calculation, we consider both ${3}_{c}\ensuremath{...