In this study we consider a bulk arrival single and batch service queue under (c, b) policy. Here the arrivals occur in batches and are served by a single server either one at a time or in batches. If the number of customers in the system is less than a specified level c, then the server serves the customer one at a time and if the number of customers in the system is at least c, then the server starts batch service and serves a maximum of b units in a batch. The steady state analysis of the model is considered and generating functions of the probabilities of the system states are obtained.