This paper proposes a new way to detect the targets in remote sensing images based on the tensor learning machine（TLM）.This method is based on tensor and tensor algebra.To utilize the multidimensional data of the remote sensing image

the vector-based learning machine is generalized to the tensor-based learning machine which accepts tensors as input

then the con-vex optimization theory and the alternating projection procedure are used to get the solution of the TLM.TLM is tested to target detection using the hyperspectral remote sensing data and high resolution remote sensing data.The experiments demonstrate the effectiveness of the proposed method

by comparing TLM with support vector machine

the tensor learning machine can keep a high probability of successful detection and reduce the false alarm.