Inspired by recent works on [m]-complex symmetric operator, we introduce the class of [∞,C]-symmetric operators and study various properties of this class. We study the quasi-nilpotent perturbations of [∞,C]-symmetric operator. Also, we prove that the class of [∞,C]-symmetric operators is norm closed. Finally, we characterize when product of [∞,C]-symmetric operators is also [∞,C]-symmetric operator.