Abstract: Traditional dimensionality reduction methods in face recognition are methods that reshapetensor face into a vector,which may lose the structural characteristics of the original data,leading toa relatively low identification result.We present a dimensionality reduction method———multilineardiscriminant subspace projection(MDSP)based on tensor.Our algorithm aims to use tensor to de-scribe face data directly,and project the tensor data onto the vector discriminant subspace through anew kind of projection method———tensor to vector projection(TVP).To reach this target,the algo-rithm first finds out the projection vectors(PV)that make data in the discriminant subspace get themaximum between-class scatter as well as the minimum within-class scatter.Then with the help ofPV,tensor data can be projected into the low dimensional vector data.As long as proper constraintsare given,the vector data can be the most representative feature data.The feature data is then sent tothe KNN classifier for classification.Results in experiments on databases ORL confirm the veracity ofour algorithm.