Natural circulation (NC) loops were widely used in many fields, but still limited in the instability of the loop. The instability characteristics of NC are not fully understood, such as oscillation boundary, amplitude and frequency. To understand the oscillation characteristics, experiments of two-phase natural circulation were performed for R134a in a single loop. Two types of the oscillation were observed and identified by the characteristic frequency in their oscillation spectra. The characteristic frequencies and amplitudes of the oscillations were affected by the system pressure, the heating power and the evaporator inlet subcooling. For the type 1 oscillation, with the increase of the heating power, the main characteristic frequency increased, while the oscillation amplitude decreased; with the increase of the system pressure, the oscillation frequency decreased; with the increase of the subcooling, the frequency decreased. For the type 2 oscillation, with the increase of the heating power, the main characteristic frequency increased, the oscillation amplitude increased; with the increase of subcooling, the frequency decreased, and the amplitude increased. An instability map was built based on the dimensionless numbers: the subcooling number N_sub versus the phase change number N_pch. The stable region of the system was wider at low subcooling condition. Two types of the oscillation may occur at the same time, and the stable region disappeared when subcooling number higher than 3. Combining dimensionless analysis and spectrum analysis, we divided the two-phase natural circulation into five regions in the instability map. Through the oscillation spectrum, this study provided a deep perspective for the instability of two-phase natural circulation. Also, the experimental results of this study can lay the foundation for future research.