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Exceptional points (EPs) are special singularities of non-Hermitian Hamiltonians. At an EP, two or more eigenvalues and the corresponding eigenstates coalesce. Recently, EP-based optical gyroscope near an EP was extensively investigated to improve the response to rotation. However, the highly resultant dimensionality in the eigenstate space causing from the EP-based system is sensitivity to more external perturbations, that is, the great response at EPs requires strict implementation conditions. To solve this problem, a new non-Hermitian structure was proposed that realizes an exceptional surface (EP surface) constructed of numerous EPs embedded in a high-dimensional parameter space. With respect to the isolated EPs, non-Hermitian EP surface provides additional degrees of freedom to permit the undesired perturbations (such as fabrication errors) shifts along the EP surface which corresponds to the robustness. On the other hand, the rotation will force the system away from these EPs obtaining a sensitivity enhancement of three orders of magnitude, compared to the traditional Sagnac effect rotation detecting. The EP surface system has a potential to combine robustness with enhanced sensitivity of the rotation.