We present a novel laser system with an external cavity delay feedback semiconductor laser under the control of Faraday effect. To study the chaos-control and chaos-anti-control of the laser system, we construct two types of optical path structures as two control systems of the negative feedback and the ring cavity by using the combination of the Faraday effect controller, the polarizer and the mirror. We give a physical model of laser dynamics with the delayed negative feedback or the delayed positive feedback under the control of Faraday effect. Using the Faraday effect principle of magnetic rotation and the characteristics of the system, we can achieve the double parameter control of the laser. We can shift the optical rotation angle by operating Faraday effect controller and modulate the optical delay time by performing the mirror to vary the double parameter. The laser can be controlled to a double-cycle, a tri-cycle, a multi-cycle, and beat phenomenon by using the control system of the negative feedback, etc. The periodic laser can be anti-controlled to chaos by using the control system of the ring cavity. Some control and anti-control areas formed with the distribution of magnetic rotation angular are found in the laser. For the negative feedback system under the some control cases, the chaotic laser can be controlled to some tri-cycle states between π/14 and π/9. By shifting the control parameters, the chaotic laser can be controlled to some cycle-7 states between 10π/133 and 10π/108 and another tri-cycle region is found from 10π/96 to π/8. Under other control parameters, the chaotic laser can be controlled to some cycle-8 or cycle-9 states. For the ring cavity system under the some control cases, the dual-cycle region is between π/10 and π/30, the cycle-6 region is between π/4 and π/5, the cycle-13 region is found to be from π/6 to 10π/76. In another control case, the large chaos-anti-control region is found to exist between 0 and π/12. Dynamic controls of the chaotic laser and the periodic laser are also studied while the transformation and evolution of laser states are discussed. It is found that it takes about 10 ns for one state to change into another state when the control operation is applied to the laser. The control method is very useful for studying chaos-control, new laser system and its application.