In this paper, the spoof surface plasmon polaritons (SSPPs) transmission line (TL) of periodical grooved bow-tie cells is proposed. The complex propagation constant and characteristic impedance of the SSPPs TLs and microstrip lines (MLs) are extracted using the analytical method of generalized lossy TL theory. The properties of the SSPPs TLs with different substrates and the same geometrical configuration are experimented. Then, for comparison, two ML counterparts are also experimented, which shows that the SSPPs TL is less sensitive to the thickness, dielectric constant and loss tangent of the chosen substrate below the cutoff frequency, compared with the ML ones. The single-conductor co-planar quasi-symmetry unequal power divider based on this SSPPs TL is presented in microwave frequencies. For experimental validation, the 0-dB, 2-dB, and 5-dB power dividers are designed, fabricated, and measured. Both simulated and measured results verify that the unequal power divider is a flexible option, which offers massive advantages including single-conductor co-planar quasi-symmetry structures, wide-band operation, and convenient implementations of different power-dividing ratios. Hence, it can be expected that the proposed unequal power dividers will inspire further researches on SSPPs for future design of novel planar passive and active microwave components, circuits and systems.