A call admission control (CAC) scheme based on statistical information is proposed, called the statistical CAC scheme. A conventional scheme needs to manage session information for each link to update the residual bandwidth of a network in real time. This scheme has a scalability problem in terms of network size. The statistical CAC rejects session setup requests in accordance to a pre-computed ratio, called the rejection ratio. The rejection ratio is computed by using statistical information about the bandwidth requested for each link so that the congestion probability is less than an upper bound specified by a network operator. The statistical CAC is more scalable in terms of network size than the conventional scheme because it does not need to keep accommodated session state information. Numerical results show that the statistical CAC, even without exact session state information, only slightly degrades network utilization compared with the conventional scheme.