Computation of flow in natural channels is the key to the solution of numerous engineering problems particularly at the time of flood. Therefore, different approaches have been incorporated for accurate estimation of flow discharge in compound meandering channels. The present work focuses on developing an empirical model for estimating the flow of meandering compound channels using gene-expression programming (GEP) by considering four non-dimensional parameters viz Relative Depth, Sinuosity, Coherence Parameter, and Discharge Ratio (Qvdm/Qbf). The model developed for the meandering compound channels is best suited for sinuosity in the range of 1.04–2. To measure adequacy of the model, the results of the developed model are compared with various discharge estimation methods such as the Single Channel Method (SCM), Divided Channel Method (DCM), Meander Belt Method (MBM), Modified Divided Channel Method (MDCM), Interacting Divided Channel Method (IDCM), and Coherence Method (COHM). Results indicate that the proposed GEP model predicted the ratio of total discharge in compound channel (Qt) to the bank-full discharge (Qbf) in main channel satisfactorily with root mean square error of 0.15 and 0.19 for training and testing dataset, respectively. The developed model is also used to validate with higher sinuous channels having sinuosity exceeding 2.0. Finally, the model was successfully validated with natural flood conditions of River Baitarani, India (sinuosity of 1.334) giving the minimum errors in terms of mean absolute square error of 0.885 and 0.882 for the two overbank flow depths of 7.5 and 8.63 m, respectively. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.