We propose a novel molecular junction with single walled carbon nanotube (SWNT) as electrodes bridged by an anthracene molecule. It is found that when the coupling between the molecule and the SWNT is noncovalent, the current-voltage (I-V) curve shows a striking nonlinear feature and a large negative differential resistance (NDR) at small bias. While in covalent adsorption site, the I-V curve behaves nearly linear. Theoretical studies based on the nonequilibrium Green's function method demonstrate that mechanism of the NDR is due to the narrow features of the local density of states (LDOS) of the SWNT as well as the alignment between the peak of LDOS of the electrodes and the molecular energy levels.