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Researchers have a special fondness for continuum robots (CRs) due to their various applications. CRs have been modeled in different ways. One of these methods is called lumped model. Although the lumped modeling of CRs needs multiple degrees of freedom, researchers have considered only a few degrees of freedom. But considering such structures led to some issues in the accuracy of the controller. Therefore, in this paper, the dynamic modeling of a CR which is based on the lumped model is developed in a general form. Additionally, a control strategy based on sliding mode back-stepping control is proposed after introducing the first and second Lyapunov functions for stability proof. Moreover, a new function in the control law is used to avoid chattering phenomena. The proposed controller can reduce the settling time, which is one of the most important factors in controlling such robots. To demonstrate the efficiency of the proposed method, three different case studies are conducted for a planar 8-DOF continuum manipulator and the simulations are compared with the feedback linearization method (FL). The simulations show the effectiveness of the proposed method for controlling the continuum robot.