The establishment of vibration differential equation is the premise and an important part for structural dynamics research. According to Euler Bernoulli beam theory, taking into account the influence of angular moment of inertia, through simultaneous geometric deformation coordination equation and internal force balance equation, the out of plane normal bending and axial torsional vibration differential equation of curved beam are derived, and the out of plane deflection control equation of curved beam is obtained. The research results provide a theoretical basis for the dynamic study of curved beam.