Recently large size color TV and computer monitor are very popular and a lot techniques are being developed to get a high quality picture on the screen through reducing the convergence error among the red, green and blue beams and achieving a high focusing. One of the techniques is considering the mutual effects of the components of the Brown tube. The magnetic deflection yoke, especially, stands immediately next to the electron gun and generates the leakage magnetic fields at the electron gun which affects the trajectories of the electron beams inside the gun. Hence a shield cup made of thin conducting plate is located at the end of electron gun in order to shield the leakage flux from the deflection yoke. Since the red, green and blue beams are placed unsymmetrically the shielding effects of the shield cup on the beams are not same and eddy current controller, made of thin conducting plate, is auxiliary placed inside the shield cup. In this paper a transient magnetic field analysis algorithm is developed using boundary element method, and applied to the analysis of the shielding effects of the eddy current controller of shield cup in an electron gun.