This article introduces a robust adaptive Lomb periodogram (RALP) for time-frequency (TF) analysis of a time series with sinusoidal and transient components, which are possibly non-uniformly sampled. It extends the conventional Lomb spectrum by windowing the observation data and adaptively selects the window lengths by the intersection of confidence intervals (ICI) rule. The influence of transient components on the conventional time-frequency representation can be moderated using M-estimation of robust statistics. Instead of treating the transient components as impulsive noise and removing them, the proposed RALP TF distribution yields separately a time domain representation of the transient components and a conventional TF representation of the sinusoidal components, which greatly improves the visualization and detection of these components. Simulation results show that the proposed RALP differentiates the two kinds of components well, and offers better time and frequency resolutions than the conventional Lomb periodogram.