In the present paper a statistical method using probability density function has been applied to investigate experimentally the flow patterns and fluctuations of time-averaged local void fraction in air-water two-phase mixtures which flow vertically upwards in concentric annuli. This study was carried out using three vertical concentric annuli. The annular test section consists of a lucite outer tube whose inside diameter is 38mm and a stainless steel inner rod. The rod diameter is either 12mm, 16mm or 20mm. The two-phase flow patterns observed in the experiment were bubbly, slug, annular and each transition patterns. It was first demonstrated that the variance, coefficients of skewness and kurtosis calculated from probability density function on time-averaged local void fraction can be used to identify the flow patterns in the annular passage, and the fluctuation of time-averaged local void fraction varies with the radial position in annular gap and the flow pattern.