Based on the Coriolis acceleration and the Lagrangian strain formula, a generalized equation for the transverse vibration system of convection belts is derived using Newton’s second law. The method of multiple scales is directly applied to the governing equations, and an approximate solution of the primary parameter resonance of the system is obtained. The detuning parameter, cross-section area, elastic and viscoelastic parameters, and axial moving speed have a significant influences on the amplitudes of steady-state response and their existence boundaries. Some new dynamical phenomena are revealed.