Numerous methods for style transfer have been developed using unsupervised learning and gained impressive results. However, optimal style transfer cannot be conducted from a global fashion in certain style domains, mainly when a single target-style domain contains semantic objects that have their own distinct and unique styles, e.g., those objects in the anime-style domain. Previous methods are incongruent because the unsupervised learning can not provide the semantic mappings between the multi-style objects according to their unique styles. Thus, in this paper, we propose a pseudo-supervised learning framework for the semantic multi-style transfer (SMST), which consists of (i) a pseudo ground truth (pGT) generation phase and (ii) a SMST learning phase. In the pGT generation phase, multiple semantic objects of the photo images are separately transferred to the target-domain object styles in an object-oriented fashion. Then the transferred objects are composed back to an image, which is the pGT. In the SMST learning phase, a SMST network (SMSTnet) is trained with the pairs of the photo images and its respective pGT in a supervised manner. From this, our framework can provide the semantic mappings of multi-style objects. Moreover, to embrace the multi-styles of various objects into a single generator, we design the SMSTnet with channel attentions in conjunction with a discriminator dedicated to our pseudo-supervised learning. Our method has been applied and intensively tested for anime-style transfer learning. The experimental results demonstrate the effectiveness of our method and show its superiority compared to the state-of-the-art methods.