We consider a discrete memoryless broadcast channel consists of two users and a sender. The sender has two independent confidential messages for each user. We extend the work of Liu et al.\ on broadcast channels with two confidential messages with weak secrecy criterion to strong secrecy. Our results are based on an extension of the techniques developed by Hou and Kramer on bounding Kullback-Leibler divergence in context of \textit{resolvability} and \textit{effective secrecy}.