The evolution of two-component cold atoms on a ring with quasispin-orbit (qSO) coupling and spin-flip has been studied analytically (for arbitrary particle number $ N $ without interaction) and numerically (for a few-body system with interaction). Counter-propagating and oscillating persistent spin-currents have been found. The regularity governing the period and amplitude of oscillation has been clarified. When the strengths for the qSO coupling and spin-flip are fixed, the frequency of oscillation can be effectively tuned by the Raman detuning, while the amplitude can be tuned by either changing the initial status and/or the Raman detuning. When the initial numbers of atoms of the two-components $N_{1}$ and $N_{2}$ are close to each other, the oscillation will be seriously suppressed. The condition for maximizing the amplitude of oscillation is given.
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