In the next generation high-speed wireless networks, it is important to provide quality-of-service (QoS) guarantees as they are expected to support multimedia applications. This paper proposes an admission control scheme based on adaptive bandwidth reservation to provide QoS guarantees for multimedia traffic carried in high-speed wireless cellular networks. The proposed scheme allocates bandwidth to a connection in the cell where the connection request originates and reserves bandwidth in all neighboring cells. When a user moves to a new cell and a handoff occurs, bandwidth is allocated in the new cell, bandwidth is reserved in the new cell's neighboring cells, and reserved bandwidth in more distant cells is released. The amount of bandwidth to reserve is dynamically adjusted, reflecting the current network conditions. The performance of the proposed scheme is evaluated through simulations of realistic cellular environments. The simulated network consists of a large number of cells, mobile users with various movement patterns are assumed, and a variety of multimedia applications (e.g., audio phone, video conference, video on demand, file transfer, etc.) is considered. It is shown that the proposed scheme provides small handoff dropping probability (i.e., the probability that handoff connections are dropped due to a lack of bandwidth) and achieves high bandwidth utilization.