We report observation of coherent oscillations in the relaxation dynamics of an exciton-polariton condensate driven by parametric scattering processes. As a result of the interbranch scattering scheme and the nonlinear polariton-polariton interactions, such parametric scatterings exhibit high scattering efficiency, which leads to fast depletion of the polariton condensate and periodic shut-off of the bosonic stimulation processes, eventually causing relaxation oscillations. Employing polariton-reservoir interactions, the oscillation dynamics in the time domain can be projected onto the energy space. In theory, our simulations using the open-dissipative Gross-Pitaevskii equation are in excellent agreement with experimental observations. Surprisingly, the oscillation patterns are clearly visible in our time-integrated images including many excitation pulses, implying the high stability of the relaxation oscillations driven by polariton parametric scatterings.