This paper presents a quality-of-service (QoS) provisioning dynamic connection-admission control (CAC) algorithm for multimedia wireless networks. A multimedia connection consists of several substreams (i.e., service classes), each of which presets a range of feasible QoS levels (e.g., data rates). The proposed algorithm is mainly devoted to finding the best possible QoS levels for all the connections (i.e., QoS vector) that maximize resource utilization by fairly distributing wireless resources among the connections while maximizing the statistical multiplexing gain (i.e., minimizing the blocking and dropping probabilities). In the case of congestion (overload), the algorithm uniformly degrades the QoS levels of the existing connections (but only slightly) in order to spare some resources for serving new or handoff connections, thereby naturally minimizing the blocking and dropping probabilities (it amounts to maximizing the statistical multiplexing gain). The algorithm employs a Hopfield neural network (HNN) for finding a QoS vector. The problem itself is formulated as a multi-objective optimization problem. Hardware-based HNN exhibits high (computational) speed that permits real time running of the CAC algorithm. Simulation results show that the algorithm can maximize resource utilization and maintain fairness in resource sharing, while maximizing the statistical multiplexing gain in providing acceptable service grades. Furthermore, the results are relatively insensitive to handoff rates.