Generalized zero-shot skeleton-based action recognition (GZSSAR) is a new challenging problem in computer vision community, which requires models to recognize actions without any training samples. Previous studies only utilize the action labels of verb phrases as the semantic prototypes for learning the mapping from skeleton-based actions to a shared semantic space. However, the limited semantic information of action labels restricts the generalization ability of skeleton features for recognizing unseen actions. In order to solve this dilemma, we propose a multi-semantic fusion (MSF) model for improving the performance of GZSSAR, where two kinds of class-level textual descriptions (i.e., action descriptions and motion descriptions), are collected as auxiliary semantic information to enhance the learning efficacy of generalizable skeleton features. Specially, a pre-trained language encoder takes the action descriptions, motion descriptions and original class labels as inputs to obtain rich semantic features for each action class, while a skeleton encoder is implemented to extract skeleton features. Then, a variational autoencoder (VAE) based generative module is performed to learn a cross-modal alignment between skeleton and semantic features. Finally, a classification module is built to recognize the action categories of input samples, where a seen-unseen classification gate is adopted to predict whether the sample comes from seen action classes or not in GZSSAR. The superior performance in comparisons with previous models validates the effectiveness of the proposed MSF model on GZSSAR.