This study aimstodeterminethe effectiveness of learning strategy and studensts? critical thinking ability in students? achievement of geometrystudent of Mathematics Study Program of Hamzanwadi University. The approach employed in this research wasquasi experiment with treatment by level design of 2 x 2. The targeted participant was students of mathematics study program of Hamzanwadi Universityin Academic Year which consists of three classes. Randomly selected two classes by each 32 participants were given to Learning Group Investigatian and Problem Based Learning. The data gained from this study are critical thinking and students? achievement in Geometry. These data were analysed by Anova. The research depicted that (1) there was no difference learning achievement withlearning group investigation and problem based-learning, (2) there was significant effectiveness between learning strategies and critical thinking abilityin students? learning achievement of Geometry, (3) studentshaving high critical thinking ability obtained better learning achievement usinglearning group investigation compared to the problem based-learning (4) there was better learning achievement usingLearning Group Investigatian compared to the Problem Based-Learning for those students having low critical thinking ability.