ATM (asynchronous transfer mode) systems can support services with bursty traffic. An ATM system needs a sophisticated and real-time connection admission controller not only to guarantee the required quality-of-service (QoS) for existing calls but also to raise the system efficiency. The input process has a power-spectral-density (PSD) which explicitly contains the correlation behavior of input traffic and has a great impact on the system performance. Also, a neural network has been widely applied to deal with traffic control related problems in ATM systems because of its self-learning capability. We propose a PSD-based neural-net connection admission control (PNCAC) method for an ATM system. Under the QoS constraint, we construct a decision hyperplane of the connection admission control according to parameters of the power spectrum. We further adopt the learning/adapting capabilities of the neural network to adjust the optimum location of the boundary between these two decision spaces. Simulation results show that the PNCAC method provides a superior system utilization over the conventional CAC schemes by as much as 18%, while keeping the QoS contract.