The near-field samples (NFSs) of base-station antennas are obtained by a circular array of probes (CAP) in spherical array sampling systems. In order to reduce sampling time, this paper proposes a compressive spherical array sampling technique based on pseudo-skeleton tensor approximation (PSTA). Specifically, the Huygens’ principle and the method of moments are applied to construct a tensor-based radiation model. Then the skeleton sampling positions of CAP are decided via PSTA of the tensor model. In the proposed method, NFSs in non-skeleton sampling positions can be computed from those in skeleton sampling positions, which realizes the compression of NFSs and thus reduces the sampling effort. Since the proposed model-driven method is independent of sampling data and provides the deterministic sampling positions, it is attractive to multi-beam antennas, especially with dynamic beamforming techniques. Moreover, a fast algorithm is developed to accelerate PSTA of the tensor model. Numerical experiments show that the proposed method can find the skeleton sampling positions with high computation efficiency and reduce the number of samples by 50% compared with uniform sampling.