Traffic prediction facilitates intelligent networking maintenance by enabling efficient network resource allocation. With the development of machine learning algorithms, traffic prediction has attracted increasing attention and has been widely used in resource allocation and traffic management. In this paper, we consider an input traffic with a quality of service (QoS) requirement, such as the overflow probability, and propose an adaptive bandwidth allocation method based on the Gaussian process regression (GPR) to satisfy the required QoS. In the proposed method with GPR, we consider the stochastic property of each sample path individually and compute the required bandwidth adaptively for each sample path by estimating its overflow probability. Thus, it is more beneficial than the bandwidth allocation method based on the average overflow probability over all sample paths that are widely used in many previous works. We investigate the computational complexity and performance of the proposed method through simulation with real-world traffic as well as computer-generated traffic and show that the proposed method allocates the bandwidth adaptively and efficiently to satisfy the required QoS.