Arched section consisted of a rectangle and a semicircle part. It is commonly applied in the field of hydroelectric engineering. The normal water depth computation equation for an arched tunnel is a transcendental equation and no analytic solution. In this paper, based on the mathematics transformation for the basis equation and the relationship analysis between the dimensionless normal water depth and the relative parameters, a new linear solution formula are established for the calculation of normal water depth for arched section tunnel according to the fitting principle. This method overcomes the shortage of other iterative trial calculating methods, such as complex calculation step, depend on the special chart and curve, and existed serious error. The new formula is simply and the maximum error is less than 0.6156% under the general engineering design range (ratio of normal water depth and arch radius is between 1 to 1.5416). it can be used on the engineering designing practice and the edit of the handbook of hydraulic structure design.