Determination of stage-discharge relationships in natural rivers is extremely important in flood control projects. The importance of rating curves in rivers and the difficulty of its establishment show the need for simpler and more precise methods. Determination of rating curves in compound channels, especially with composite roughness, has proved to be difficult because of significant variations in hydraulic parameters from the main channel to the floodplains. In the current paper, a new approach that is based on the concept of the cross-sectional isovel contours is introduced for estimation of the stage-discharge curves in compound channels. The multivariate Newton's method is applied to the difference between the observed and estimated data to optimize the exponent values of the governing parameters. The proposed method is verified by comparing predictions obtained by using it with some experimental datasets. For compound channels with composite roughness, the stage-discharge curves obtained by the proposed method are more accurate than those obtained by using available conventional methods.