Since metallic nanowires can confine light in nanoscale beyond the diffraction limit, metallic nanowires play an important role in nanophotonic integrated circuits. In this paper, a silver nanowire waveguide with a cross is proposed and its surface plasmon polaritons (SPPs) splitting properties of the cross at λ = 532 nm are studied by the finite element method. The nanowire has a square shape with its side length of a. Results show that the outputs for different input modes depend on the geometric parameters of the nanowires. For SPPs with TM0 mode, there are similar intensities in different waveguide directions with smaller side length. With the increase of a, the intensity in the original waveguide direction increases monotonically, and those in the perpendicular direction will decrease monotonically. For SPPs with HE1 mode and HE-1 mode, most of the energy propagate along the original waveguide direction for smaller a. With the increase of a, the intensity in the original waveguide direction decreases dramatically. For SPPs with HE1 mode, the cross blocks most of the energy in three directions for larger a. In addition to the splitting effect of it, the cross also performs a function of mode conversion. For the input SPPs with TM0 mode, the output of SPPs along the perpendicular waveguide direction can be converted to the HE-1 mode. For the input SPPs with HE1 mode, the output of SPPs along the perpendicular waveguide direction can be converted to the TM0 mode. Due to the superposition of electric fields of different SPPs modes in the perpendicular waveguide direction occur the steady-state and periodic electric field distributions.