Problem-solving strategies, defined as actions people select intentionally to achieve desired objectives, are distinguished from skills that are implemented unintentionally. In education, strategy-oriented instructions that guide students to form problem-solving strategies are found to be more effective for low-achievement students than the skill-oriented instructions designed for enhancing the skill implementation ability. However, conventional cognitive diagnosis models (CDMs) seldom distinguish the concept of skills from strategies. While the existing longitudinal CDMs can model students’ dynamic skill mastery status change over time, they did not intend to model the shift in students’ problem-solving strategies. Thus, it is hard to use conventional CDMs to identify students who need strategy-oriented instructions or evaluate the effectiveness of the education intervention programs that aim at training students’ problem-solving strategies. This study proposes a longitudinal CDM that takes into account both between-person multiple strategies and within-person strategy shift. The model, separating the strategy choice process from the skill implementation process, is intended to provide diagnostic information on strategy choice as well as skill mastery status. A simulation study is conducted to evaluate the parameter recovery of the proposed model and investigate the consequences of ignoring the presence of multiple strategies or strategy shift. Further, an empirical data analysis is conducted to demonstrate the use of the proposed model to measure strategy shift, growth in the skill implementation ability and skill mastery status.