The active appearance model (AAM) is a well-known model that can represent a non-rigid object effectively. However, the fitting result is often unsatisfactory when an input image deviates from the training images due to its fixed shape and appearance model. To obtain more robust AAM fitting, we propose a tensor-based AAM that can handle a variety of subjects, poses, expressions, and illuminations in the tensor algebra framework, which consists of an image tensor and a model tensor. The image tensor estimates image variations such as pose, expression, and illumination of the input image using two different variation estimation techniques: discrete and continuous variation estimation. The model tensor generates variation-specific AAM basis vectors from the estimated image variations, which leads to more accurate fitting results. To validate the usefulness of the tensor-based AAM, we performed variation-robust face recognition using the tensor-based AAM fitting results. To do, we propose indirect AAM feature transformation. Experimental results show that tensor-based AAM with continuous variation estimation outperforms that with discrete variation estimation and conventional AAM in terms of the average fitting error and the face recognition rate.