This work presents a proposed controller based on a generalized linear extended state observer (GLESO) for continuum robots (CR) facing unmatched uncertainties in trajectory tracking. The complex structure of CRs makes accurate modeling difficult, especially when operating in unknown environments. Internal and external uncertainties further impact the control performance, particularly the unmatched uncertainties. To address this, the GLESO is employed to observe and compensate for the unmatched uncertainties. Additionally, a tailored slide mode controller (SMC) is introduced to achieve stabilized control. Numerical simulations are conducted to validate the effectiveness of the proposed method.