In this “info-plosion” era, recommendation systems (or recommenders) play a significant role in finding interesting items in the surge of on-line digital activities and e-commerce. Several techniques have been widely applied for recommendation systems, but the cold start and sparsity problems remain a major challenge. The cold start problem occurs when generating recommendations for new users and items without sufficient information. Sparsity refers to the problem of having a large amount of users and items but with few transactions or interactions. In this paper, a novel cross-domain recommendation model, Cross-Domain Evolution Learning Recommendation (abbreviated as CD-ELR), is developed to communicate the information from different domains in order to tackle the cold start and sparsity issues by integrating matrix factorization and recurrent neural network. We introduce an evolutionary concept to describe the preference variation of users over time. Furthermore, several optimization methods are developed for combining the domain features for precision recommendation. Experimental results show that CD-ELR outperforms existing state-of-the-art recommendation baselines. Finally, we conduct experiments on several real-world datasets to demonstrate the practicability of the proposed CD-ELR.