Sequential recommendation (SR) aims to predict the next purchasing item according to users' dynamic preference learned from their historical user-item interactions. To improve the performance of recommendation, learning dynamic heterogeneous cross-type behavior dependencies is indispensable for recommender system. However, there still exists some challenges in Multi-Behavior Sequential Recommendation (MBSR). On the one hand, existing methods only model heterogeneous multi-behavior dependencies at behavior-level or item-level, and modelling interaction-level dependencies is still a challenge. On the other hand, the dynamic multi-grained behavior-aware preference is hard to capture in interaction sequences, which reflects interaction-aware sequential pattern. To tackle these challenges, we propose a Multi-Grained Preference enhanced Transformer framework (M-GPT). First, M-GPT constructs a interaction-level graph of historical cross-typed interactions in a sequence. Then graph convolution is performed to derive interaction-level multi-behavior dependency representation repeatedly, in which the complex correlation between historical cross-typed interactions at specific orders can be well learned. Secondly, a novel multi-scale transformer architecture equipped with multi-grained user preference extraction is proposed to encode the interaction-aware sequential pattern enhanced by capturing temporal behavior-aware multi-grained preference . Experiments on the real-world datasets indicate that our method M-GPT consistently outperforms various state-of-the-art recommendation methods.