We propose Piecewise Locally Stationary Oscillation (PLSO) state-space model for decomposing nonstationary time series with slowly time-varying spectra into several oscillatory, piecewise-stationary processes. PLSO combines piecewise stationarity in classical signal processing and stationary Gaussian process kernels, effectively addressing the drawbacks of these ideas, such as inefficient inference and discontinuous/distorted estimates across stationary interval boundaries.