This paper is devoted to study the circular geodesics of the dyonic Kerr-Newman black hole with a cosmic string passing through it. We investigate circular geodesics of null and timelike particle. In this context, we find the circular photon orbit as well as the innermost stable circular orbit. The angular velocity and time period for the timelike particle are calculated. The effect of electric and magnetic charge as well as of the cosmic string parameter on the effective potential is analyzed numerically. Finally, we discuss the role of these parameters on the energy extraction by the Penrose process. We conclude that the string parameter does not affect the gain energy of the particle but it decreases with respect to charge.