A nanostructure of broadband surface plasmons logic AND gate was presented. The two input ports were composed of broadband infrared directional couplers which were a pair of two parallel slot nano-antennas milled into gold film. An array of couplers arranged on an arc-shaped circle was capable of focusing the surface plasmons to the circular center when it was illuminated with radially polarized beam. The same two focused surface plasmons spots were coupled into two groove-shaped waveguides, respectively, and then interfered each other at the cross point. The intensity was four times that of intensity produced by a single arc-shaped nanostructure when two arc-shaped nanostructures produced the surface plasmons in the center with the same amplitude, polarization direction and zero phase difference. The nanostructure and device principle were theoretically analyzed. The relation between input ports and output port along with broadband property were simulated with the finite difference in time domain method.