There exists an increasing demand by an ever-growing number of mobile customers for transfer of rich media contents such as video conferencing, file transfer and retrieval service, e-mail, paging, fax in addition to simple voice calls. This requires very high bandwidth that cannot be provided by the current cellular systems maintaining quality of service (QoS) because of limited bandwidth capacity. In this paper, a new adaptive call admission control scheme is proposed for allocating bandwidth optimally as well as provisioning QoS to the mobile users so far as practicable. In addition to these services, the proposed scheme during congestion also attempts to maximise the number of served calls in a cell to satisfy maximum number of users. Extensive simulation results show that the proposed scheme outperforms the existing schemes in terms of call blocking probability, system delay and bandwidth utilisation.