Session-based recommendation (SBR) aims to predict the following item a user will interact with during an ongoing session. Most existing SBR models focus on designing sophisticated neural-based encoders to learn a session representation, capturing the relationship among session items. However, they tend to focus on the last item, neglecting diverse user intents that may exist within a session. This limitation leads to significant performance drops, especially for longer sessions. To address this issue, we propose a novel SBR model, called Multi-intent-aware Session-based Recommendation Model (MiaSRec). It adopts frequency embedding vectors indicating the item frequency in session to enhance the information about repeated items. MiaSRec represents various user intents by deriving multiple session representations centered on each item and dynamically selecting the important ones. Extensive experimental results show that MiaSRec outperforms existing state-of-the-art SBR models on six datasets, particularly those with longer average session length, achieving up to 6.27% and 24.56% gains for MRR@20 and Recall@20. Our code is available at https://github.com/jin530/MiaSRec.