A kind of surface plasmon polariton (SPP) directional coupler in which metal strip between the two adjacent waveguides is thinner than the metal film is simulated by using three dimensional full-vectorial finite difference time-domain (FDTD) method. The distributions of electromagnetic field and longitudinal energy flux density when only fundamental mode propagates in waveguides are analysed, and the dependences of coupling length and maximum transfer power on the height of metal strip are discussed. Results show that the energy flux density along the propagation direction distributions mainly in the part near the metal strip, which is beneficial to increase the coupling strength. Also, the efficient decrease of coupling length in directional coupler can be achieved by reducing the height of metal strip between waveguides. This sub-wavelength of directional coupler can be applicable for the optical integrated circuit based on surface plasmon polaritons.