In recommender systems, cold-start is a long-standing problem. To solve this problem, cross-domain recommendation methods transfer domain-shared feature from source domain to make recommendations in target domain. Existing methods take the features that a user presents in both domains as domain-shared. However, due to the data sparsity problem, users often present domain-shared features only in one domain, and existing methods may loss these valuable misaligned domain-shared features. To solve this issue, we propose a Misaligned Domain-shared feature aware method for Cross-Domain cold-start Recommendation (MDCDR). The domain-shared feature distillation module applies two complementary tasks to extract misaligned domain-shared features. The misaligned feature probing module tests and discards domain-specific features by a data augmentation and a mixture recommendation task. As a result, MDCDR gains comprehensive misaligned domain-shared features for cross-domain recommendation. Extensive experiments on two cross-domain datasets show that MDCDR outperforms various state-of-the-art methods.