In a double-gap coupled cavity of klystrons, the electrons exchange energy with the electric field in each gap through beam-wave interaction process, and different beam-loading effects take place in each gap. However in this case the traditional beam-loading model does not hold true. To solve this problem, we present a novel model according to the space-charge-wave theory to calculate the beam-loading conductance in each gap of the coupled-cavity, and also derive the formulations. Moreover, we perform a simulation study using a three-dimensional particle-in-cell code. The results obtained by the model show good agreement with the simulation results. In comparison with the traditional model, the new model can be used to calculate the beam-loading conductances in diffident regions of the coupled-cavity, and then it can be used to study the beam-wave interactions in the gaps and analyze the mode stability in the coupled-cavity in a high accuracy.