Recently, deep learning for image generation with a guide for the generation has been progressing. Many methods have been proposed to generate the animation of facial expression change from a single face image by transferring some facial expression information to the face image. In particular, the method of using facial landmarks as facial expression information can generate a variety of facial expressions. However, most methods do not focus on anime characters but humans. Moreover, we attempted to apply several existing methods to anime characters by training the methods on an anime character face dataset; however, they generated images with noise, even in regions where there was no change. The first order motion model (FOMM) is an image generation method that takes two images as input and transfers one facial expression or pose to the other. By explicitly calculating the difference between the two images based on optical flow, FOMM can generate images with low noise in the unchanged regions. In the following, we focus on the aspect of the face image generation in FOMM. When we think about the employment of facial landmarks as targets, the performance of FOMM is not enough because FOMM cannot use a facial landmark as a facial expression target because the appearances of a face image and a facial landmark are quite different. Therefore, we propose an advanced FOMM method to use facial landmarks as a facial expression target. In the proposed method, we change the input data and data flow to use facial landmarks. Additionally, to generate face images with expressions that follow the target landmarks more closely, we introduce the landmark estimation loss, which is computed by comparing the landmark detected from the generated image with the target landmark. Our experiments on an anime character face image dataset demonstrated that our method is effective for landmark-guided face image generation for anime characters. Furthermore, our method outperformed other methods quantitatively and generated face images with less noise.