Hierarchical Multi-Label Classification (HMC) is a challenging task in data mining and machine learning. Each instance in HMC can be classified into two or more classes simultaneously. These classes are structured in a hierarchy, in the form of either a tree or a directed acyclic graph. Therefore, an instance can be assigned to two or more paths from the hierarchical structure, resulting in a complex classification problem with hundreds or thousands of classes. Several methods have been proposed to deal with such problems, including several algorithms based on well-known bio-inspired techniques, such as neural networks, ant colony optimization, and genetic algorithms. In this work, we propose a novel global method called GEHM, which makes use of grammatical evolution for generating HMC rules. In this approach, the grammatical evolution algorithm evolves the antecedents of classification rules, in order to assign instances from a HMC dataset to a probabilistic class vector. Our method is compared to bio-inspired HMC algorithms in protein function prediction datasets. The empirical analysis conducted in this work shows that GEHM outperforms the bio-inspired algorithms with statistical significance, which suggests that grammatical evolution is a promising alternative to deal with hierarchical multi-label classification of biological data.