In our manuscript, we investigate the interior approximate controllability for the subsequent semilinear second-order system in L 2 ( Ω ) s ″ ( σ ) + A 0 s ( σ ) = B 0 u ( σ ) + ξ ( σ , s ( σ ) ) , 0 ≤ σ ≤ ϱ s ( 0 ) = s 0 , s ′ ( 0 ) = s 1 , where A 0 is the linear and unbounded operator, B 0 is a bounded linear operator and ξ is a nonlinear operator defined on appropriate spaces. The proposed problem can be converted into an equivalent first-order semilinear control system, then the approximate controllability results for the proposed system are obtained from the study of the approximate controllability of the reduced first-order system. The Leray–Schauder alternative theorem and principle of contraction are used in the proof of our main theorems.