Consider a single server retrial queueing system with second optional service under non-pre-emptive priority service in which two types of customers arrive in a Poisson process. In this model the server provides two types of services that are Essential Service and Second Optional Service. The essential service will be given first to both low priority and high priority customers. This second optional service will be extended to only high priority customers if they demand. The various systems measures have been calculated like Mean number of customers in the orbit, Mean number customers in the queue, Probabilities of server idle, busy etc