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This paper introduces the kernel constrained mutual subspace method (KCMSM) and provides a new framework for 3D object recognition by applying it to multiple view images. KCMSM is a kernel method for classifying a set of patterns. An input pattern x is mapped into the high-dimensional feature space $\cal{F}$ via a nonlinear function φ, and the mapped pattern φ(x) is projected onto the kernel generalized difference subspace, which represents the difference among subspaces in the feature space $\cal{F}$. KCMSM classifies an input set based on the canonical angles between the input subspace and a reference subspace. This subspace is generated from the mapped patterns on the kernel generalized difference subspace, using principal component analysis. This framework is similar to conventional kernel methods using canonical angles, however, the method is different in that it includes a powerful feature extraction step for the classification of the subspaces in the feature space $\cal{F}$ by projecting the data onto the kernel generalized difference subspace. The validity of our method is demonstrated by experiments in a 3D object recognition task using multiview images.