Continuous offline reinforcement learning (CORL) combines continuous and offline reinforcement learning, enabling agents to learn multiple tasks from static datasets without forgetting prior tasks. However, CORL faces challenges in balancing stability and plasticity. Existing methods, employing Actor-Critic structures and experience replay (ER), suffer from distribution shifts, low efficiency, and weak knowledge-sharing. We aim to investigate whether Decision Transformer (DT), another offline RL paradigm, can serve as a more suitable offline continuous learner to address these issues. We first compare AC-based offline algorithms with DT in the CORL framework. DT offers advantages in learning efficiency, distribution shift mitigation, and zero-shot generalization but exacerbates the forgetting problem during supervised parameter updates. We introduce multi-head DT (MH-DT) and low-rank adaptation DT (LoRA-DT) to mitigate DT's forgetting problem. MH-DT stores task-specific knowledge using multiple heads, facilitating knowledge sharing with common components. It employs distillation and selective rehearsal to enhance current task learning when a replay buffer is available. In buffer-unavailable scenarios, LoRA-DT merges less influential weights and fine-tunes DT's decisive MLP layer to adapt to the current task. Extensive experiments on MoJuCo and Meta-World benchmarks demonstrate that our methods outperform SOTA CORL baselines and showcase enhanced learning capabilities and superior memory efficiency.