Aiming at the shortcomings of traditional vibrating screens with large vibration mass, a double eccentric cam self-synchronous vibrating screen is proposed. The motion differential equation of the vibrating screen system is derived by using Lagrange equation and the steady state solution is obtained. According to Hamilton principle, the synchronization condition of the vibration system is deduced, and the stability condition of the self-synchronization motion is obtained. The influencing factors of synchronization and stability are investigated by using numerical calculation and simulation analysis methods. The results show that stable self-synchronous motion of the vibration system is implemented when the synchronization and stability conditions are satisfied; the value of the stable phase difference of two cams varies in the range of (–1.5 rad, 0), and compared with the residual torque difference, the eccentricity of eccentric cams has a greater impact on the stable phase difference; additionally, a linear motion track of the vibrating screen is achieved.