Few-shot classification aims to classify samples with a limited quantity of labeled training data, and it can be widely applied in practical scenarios such as wastewater treatment plants and healthcare. Compared with traditional methods, existing deep metric-based algorithms have excelled in few-shot classification tasks, but some issues need to be further investigated. While current standard convolutional networks can extract expressive depth features, they do not fully exploit the relationships among input sample attributes. Two problems are included here: (1) how to extract more expressive features and transform them into attributes, and (2) how to obtain the optimal combination of sample class attributes. This paper proposes a few-shot classification method based on manifold metric learning (MML) with feature space embedded in symmetric positive definite (SPD) manifolds to overcome the above limitations. First, significant features are extracted using the proposed joint dynamic convolution module. Second, the definition and properties of Riemannian popular strictly convex geodesics are used to minimize the proposed MML loss function and obtain the optimal attribute correlation matrix A. We theoretically prove that the MML is popularly strictly convex in the SPD and obtain the global optimal solution in the closed space. Extensive experimental results on popular datasets show that our proposed approach outperforms other state-of-the-art methods.