We have grown single crystals of Na$_2$BaNi(PO$_4$)$_2$, a new spin-1 equilateral triangular lattice antiferromagnet (ETLAF), and performed magnetic susceptibility, specific heat and thermal conductivity measurements at ultralow temperatures. The main results are (i) at zero magnetic field, Na$_2$BaNi(PO$_4$)$_2$ exhibits a magnetic ordering at 430 mK with a weak ferromagnetic moment along the $c$ axis. This suggests a canted 120$^circ$ spin structure, which is in a plane including the crystallographic $c$ axis due to the existence of an easy-axis anisotropy and ferromagnetically stacked along the $c$ axis; (ii) with increasing field along the $c$ axis, a 1/3 magnetization plateau is observed which means the canted 120$^circ$ spin structure is transformed to a up up down (UUD) spin structure. With even higher fields, the UUD phase further evolves to possible V and V phases; (iii) with increasing field along the $a$ axis, the canted 120$^circ$ spin structure is possibly transformed to a umbrella phase and a V phase. Therefore, Na$_2$BaNi(PO$_4$)$_2$ is a rare example of spin-1 ETLAF with single crystalline form to exhibit easy-axis spin anisotropy and series of quantum spin state transitions.
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