Model-based offline reinforcement learning learns a dynamics model from a static dataset and uses model-generated samples to assist policy optimization, providing a feasible solution for high-risk and high-cost decision-making problems in the real world. However, existing model-based offline reinforcement learning methods face two major challenges: insufficient coverage of the static dataset leads to cognitive error between the empirical Bellman operator and the true Bellman operator; meanwhile, error accumulation in multi-step predictions of the dynamics model causes generated virtual samples to introduce model hallucinations, further exacerbating bias in value estimation. To address these issues, this paper proposes a Model-Based Offline Deterministic Actor-Critic with Dual-Source Uncertainty(MDSU) method. Uncertainty quantifiers are constructed for the static dataset and the dynamics model, respectively, to characterize the estimation risks associated with the two data sources. The uncertainty quantifiers are incorporated as penalty terms into the static Bellman target and the virtual Bellman target, and a dual-source uncertainty fusion operator is constructed through a weighted fusion mechanism, thereby suppressing the negative effects of both types of errors during policy evaluation. Theoretical analysis proves that when the static-data uncertainty quantifier and the dynamics-model uncertainty quantifier can effectively constrain the corresponding cognitive error, MDSU has an explicit suboptimality regret bound. Experimental results on MuJoCo continuous-control tasks show that MDSU achieves the highest normalized scores on most tasks, verifying its effectiveness in improving performance and training stability.