With the advancement of technologies in the field of communication and increasing need of one-to-many communication in different spares of life, multicast communication is becoming a challenging issue in modern communication. The main challenge of multicasting in fiber optics communication is request blocking due to finite resource in WDM optical network. In this paper we have proposed a priority search technique to route multicast sessions in a WDM mesh network. The simulation result shows that the proposed algorithm increases the throughput of communication in a delay constrained application by reducing rate of request blocking in a sparse-split constrained finite wavelength WDM mesh network.