Let X be a normal projective variety and f : X → X a non-isomorphic polarized endomorphism. We give two characterizations for X to be a toric variety. First we show that if X is Q-factorial and G-almost homogeneous for some linear algebraic group G such that f is G-equivariant, then X is a toric variety. Next we give a geometric characterization: if X is of Fano type and smooth in codi- mension 2 and if there is an f−1-invariant reduced divisor D such that f|X/D is quasi-  ́etale and KX + D is Q-Cartier, then X admits a quasi- ́etale cover X  such that X  is a toric variety and f lifts to X . In particular, if X is further assumed to be smooth, then X is a toric variety.