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A continuous‐time multi‐state Markovian deteriorating system subject to aging and fatal shocks under continuous inspection is investigated in this paper. An action is chosen from {do‐nothing, repair, replace} upon each state x transited from the resulting state after the last action and so it is state‐dependent. Henceforth, a state‐dependent maintenance policy R_i,j(T,N,α) in which two states i < j are used as thresholds to control the repair and replacement in the way that the repair (resp. replacement) is taken whenever the state x satisfies i ≤ x ≤ j – 1 (resp. j ≤ x ≤ L). The performance of this state‐dependent maintenance policy is measured in terms of the expected long run cost rate. An iterative algorithm is provided to optimize the proposed maintenance policy. A numerical example is given to illustrate the method.