This study developed a mobile-based complex puzzle game, Mast Dream, to present the content of Taiwan history in the Age of Discovery. We created a pop-up map inserted with several near field communication (NFC) tags with which students can retrieve learning content from mobile phones. The study aimed to investigate students' learning performance and their logical thinking ability after learning history with Mast Dream. The pop-up map can be spread out from its original pop-up book form into a big map describing a portion of Taiwan coast in the Age of Discovery with the content including ships, castles, and farmlands. The digital content in the mobile phone was created by Unity game engine and presented in 2D animation form. Historical narrative animations, interactive stories, mini-games, and hands-on activities were designed in the content. In the story, the student acted as a Dutch sailor working on the ship, Amsterdam, to make the great historical exploration. Different levels of logical thinking games were designed in the progressive levels. Fifteen college students in Taiwan were invited to be the participants in this study. The pre-test and post-test regarding to the learning effectiveness and logical thinking were conducted with individual interviews. The results showed that the students' knowledge to the history of the Age of Discovery has reached significant difference after playing the game. For the aspect of logical thinking ability, the students who got higher logical thinking scores in pre-test had shorter gaming time which showed natural consequence of formal transfer. However, the results showed that the students' logical thinking ability have some improvement but have not reached significant differences after playing the game since logical thinking ability cannot be trained in a short period of time. All students showed excitements and high motivation playing the game since the pop-up map is intriguing, and the digital content is in various forms. It is affirmative that mobile-based complex puzzle game has high potential to enhance the learning effectiveness.