We present second-order sufficient optimality conditions for the Mayer optimal control problem under general control constraints. For this aim we assume that neighboring controls can be approximated by second-order tangents relative to critical directions. This is always the case when the control constraints are described by functional inequalities involving \(C^2\) functions with linearly independent gradients of active constraints. Sufficient conditions are expressed then by strengthening the known inequalities of the second-order necessary conditions.