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In this paper, a new pansharpening method is proposed by constructing a set of multiscale geometric support tensor filters (MGSTFs). First, a least-square ridgelet support tensor machine is developed to derive a series of MGSTFs. Then the source images are formulated as tensors and filtered by MGSTFs to capture geometric and salient features of images. These features are then fused at each scale and direction to obtain the fused products. The distortions can be reduced by exploring the tensor formulation of multispectral data and endowing the filters' directionality to capture the geometric details of images. Some experiments are carried out on several groups of QuickBird and GeoEye-1 images, and the results show that our proposed method can simultaneously reduce spectral distortions and preserve spatial details in the fused image.