Short text similarity measurement is an important task, which is broadly applied to many fields. Due to the lack of contextual information, it is not easy to accurately compare the similarity between short texts. The relations between words are used to enhance the information. Since Graph Neural Networks (GNN) perform well in handling data with complex relations, the potential of GNN in this task has been explored recently. Unfortunately, the relationship between words is not adequately acquired by existing GNN-based methods. Furthermore, they ignore the deep relationships between words and do not take them into account. Typically, these methods use a fixed graph structure for a sentence and do not update the graph structure in the network. Based on the situation, we explore utilizing the deeper relations between words to improve the applicability of GNN for this task. In this letter, we present a framework called Word Relation-based Graph Neural Network (WRGNN). WRGNN can automatically discover and construct relations between words and reconstruct those relations in the processing. Two benchmark datasets are evaluated extensively, with WRGNN obtaining an average of 71.2 % on STS-B and 82.9 % on SICK.