Abstract: Abstract: The normal depth is an important hydraulic element for channel design, operation and management. U-shaped channel has excellent hydraulic performance and strong ability of anti-frost heave, while the normal depth in the governing equations of the current common methods is implicit and have no analytical solutions. We introduced cross section characteristic parameter and dimensionless relative normal depth and took the actual flow rate in channel as the transitional flow rate when the flow depth is exactly equal to the bottom arc height. The direct calculation formula for the normal depth in U-shaped channel was presented by Marquardt method based on the NLIN procedure using SAS software. Marquardt method was used to assess whether the fitting formula reaches the best fitting result by using the iterative program to calculate the residual sum of squares. Fitting formula is the best one when the minimum residual sum of squares exists, having the characteristics of well adaptable to formula, low requirement to iterative initial value and easy to convergence, etc. This method is an effective one to solve the question of fitting non-linear equation and one of the most popular method in the field of solving non-linear equation at present. The error analysis showed the absolute value of the relative error for the proposed formula was smaller than 0.44% when the actual flow rate in channel was smaller than the transitional flow rate. Though the relative error increases when the actual flow rate in channel was larger than the transitional flow rate, the absolute value of relative error was less than 1% in which the relative error less than 0.08% when the slope coefficient was zero, and the error increased when the slope coefficient was not equal zero, but the absolute error was below 1%. It was thus indicated that the proposed formula had high precise and satisfied the need of Engineering practice. In addition, the proposed formula, with the simple form and the clear physical concept, exhibit both simplicity, easy-to-use and strong generality because it can be used to solve the normal depth of wide-shallow channel and the narrow-deep channel. Therefore, the efficient computational tools presented in this paper will be useful in the design and management of channel.