The effects of gas (0.02-0.1 m/s) and liquid velocities (0.0-0.10 m/s) on the bubble properties and pressure fluctuations have been determined in a 0.376 m-IDx 2.1 m-high bubble column. The pressure fluctuations have been analyzed by resorting to the Fractal analysis; the time series of pressure fluctuation signals have been analyzed by means of the Rescaled range analysis and the Hurst exponent has been obtained. The bubble chord length and its rising velocity increase but the Hurst exponent decreases with increasing gas velocity. Whereas, the bubble chord length decreases, but the Hurst exponent increases with an increase in liquid velocity in the continuous bubble column (UL>0.02 m/s). The Hurst exponent has been found to have a definite relationship with the bubble chord length and its standard deviation.