The electromagnetic fields and plasma parameters have been studied in an azimuthally symmetric surface wave-excited plasma (SWP) source, by using a two-dimensional numerical analysis based on the finite-difference time-domain (FDTD) approximation to Maxwell's equations self-consistently coupled with a fluid model for plasma evolution. The FDTD/fluid hybrid simulation was performed for different gas pressures in Ar and different microwave powers at 2.45 GHz, showing that the surface waves (SWs) occur along the plasma–dielectric interfaces to sustain overdense plasmas. The numerical results indicated that the electromagnetic SWs consist of two different waves, Wave-1 and Wave-2, having relatively shorter and longer wavelengths. The Wave-1 was seen to fade away with increasing pressure and increasing power, while the Wave-2 remained relatively unchanged over the range of pressure and power investigated. The numerical results revealed that the Wave-1 propagates as backward SWs whose phase velocity and group velocity point in the opposite directions. In contrast, the Wave-2 appeared to form standing waves, being ascribed to a superposition of forward SWs whose phase and group velocities point in the same direction. The fadeaway of the Wave-1 or backward SWs at increased pressures and increased powers was seen with the damping rate increasing in the axial direction, being related to the increased plasma electron densities. A comparison with the conventional FDTD simulation indicated that such fine structure of the electromagnetic fields of SWs is not observed in the FDTD simulation with spatially uniform and time-independent plasma distributions; thus, the FDTD/fluid hybrid model should be employed in simulating the electromagnetic fields and plasma parameters in SWPs with high accuracy.