A two-segment Fermi-Pasta-Ulam lattice has been investigated by using nonequilibrium molecular dynamics. Here we present an anomalous negative differential thermal resistance (NDTR) that has not been reported in Frenkel-Kontorova and φ(4) lattices up to the present. The NDTR disappears in the low-temperature region. The region of NDTR shifts from the large to the small temperature difference region as the system size increases. The anomalous dependence of NDTR on the temperature can be explained as the negative effect induced by the nonlinear coupling. The explanation can also cover the phenomenon of NDTR in momentum-nonconserved lattices.