  In this paper we construct new hairy black holes of
Lovelock-Born-Infeld-Scalar gravity in diverse dimensions. We study horizon
structures of the black holes and find the black holes may possess three
horizons, two horizons or one horizon. We give the thermodynamic quantities and
check the first laws. We study the thermal phase transition behaviors of the
black holes in $T$-$S$ plane, and find for even-dimensional black holes, in
some ranges of the parameters Van der Waals-like phase transitions occur, in
some ranges of the parameters, reentrant phase transitions (RPTs) appear. For
odd-dimensional black holes no such phase transitions are found.
