<p>This paper examines the approximate controllability of damped second-order stochastic differential inclusions with state-dependent delay. The existence of mild solutions for the given system can be established using the cosine operators, the fixed-point theorem with stochastic analysis theory, and multivalued maps. A new set of requirements has been developed, and it has been proven that the given system is approximately controllable. Finally, an application to an approximate controllability of damped second-order stochastic differential inclusions with state-dependent delay is demonstrated to illustrate the obtained theory.</p>