With the fast development of artificial intelligence, a lot of translation methods and search methods have been proposed to address molecular optimization problems in drug design, which enables this field to achieve remarkable progress. However, existing methods still encounter great difficulties in addressing problems involving more than three properties, since these problems pose stiff challenges to translation methods and search methods in terms of acquiring high-quality training data and balancing multiple properties, respectively. In this paper, we propose an adaptive evolutionary optimization framework to address the many-property molecular optimization problems (namely MaOMO). MaOMO adaptively identifies the property with the largest improvement potential in each iteration, which generates high-quality molecules as efficiently as possible by devoting more efforts to the property. Besides, MaOMO adopts a dynamic selection strategy to select molecules with large property improvement, good property diversity, and structure diversity. We investigate the performance of MaOMO framework on both benchmark and practical molecular optimization tasks, which involve the simultaneous optimization of four or more properties. Experimental results show that the proposed framework is superior to five state-of-the-art competitors, which achieves a success rate improvement of more than 20% on practical optimization tasks.