This study investigates a method to predict the horizontal/vertical turbulence intensiities distribution in steady non-uniform flow. It deals with the deviation of these turbulence characteristics from the unifrom flow distribution. The empirical results show that the flow acceleration causes the deviation of turbulence intensities from the standard linear distrubtion. By connecting the flow acceleration with turbulence intensities, the study demonstrates empirically that the linear distrubtion of turbulence intensities can be observed when the flow acceleration is zero; the concave distribution of these characteristics can be observed when the flow acceleration is negative or when the flow velocity is decreased along the channel; the convex distribution of these characteristics can be observed when the flow acceleration is positive or the flow velocity is increased along the channel. The theorectical models are verified using the experimental data available in the literature, and good agreements between the predicted and measured profiles have been achieved.