In this study, we obtain the flow signals before and after the ONB through natural circulation experiments under pressure conditions of 0.15MPa and 0.3MPa. Researches were conducted by applying nonlinear analysis techniques. Results revealed that the power spectrum of volume flow data declined exponentially over time in semi logarithmic coordinates, the autocorrelation coefficient declined gradually and the phase diagram exerted the subtle structures of chaotic movement, which might prove the existence of chaos in natural circulation system. The natural convection of single phase appeared before the occurrence of ONB belonged to a non equilibrium process which showed remarkable random features. The occurrence of ONB was a process containing the beginning of chaotic motion and the continuing occurrence of bubbles at ONB and the tendency of phase change to become nucleation boiling would achieve certain states, which embodied the characteristics of chaos. In addition, the intense density difference environment of natural circulation could accelerate the occurrences of both chaotic motion and ONB. While the density difference of heated liquid decreased with the increase of pressure, which could delay the occurrence of ONB.