The controllability and the observability of continuous linear time-varying systems with norm-bounded parameter perturbations are analyzed in this paper, The sufficient conditions which ensure the controllability of the perturbed system are presented by using the derived state transition matrix relationship between the nominal system and the perturbed system. The proposed sufficient conditions allow the evaluation of controllability under the norm-bounded parameter perturbations. The robustness of the observability is also studied for continuous linear time-varying systems with norm bounded parameter perturbations, and the corresponding sufficient conditions are provided.