The aim of this study was to investigate the enhancement of the mathematical understanding ability of pre-service mathematics teachers through Activity-Class discussion-Exercise (ACE) teaching cyclic based on APOS theory. This study used a quasi-experiment method with non-equivalent pre-post test control group design. The subjects of this study were 120 pre-service mathematics teachers from two universities in Palembang, Indonesia. The subjects were divided into two classes, that are, experiment and control class. Experiment class was a class that is applied ACE teaching cyclic based on APOS theory, whereas control class was a class that is applied direct learning. The subjects were also divided into three groups of mathematical initial ability, that are, high, average, and low. The Instruments used in this study were mathematical initial ability test, mathematical understanding ability test, observation, and interview. Data analysis tests used in this study were statistic test of parametric and non-parametric. The results of data analysis showed that 1) there is no significant difference between the enhancement of mathematical understanding ability of pre-service mathematics teachers applied ACE teaching cyclic based on APOS theory and direct learning in terms of overall and group of mathematical initial ability, 2) there is no interaction between learning factors (ACE teaching cyclic and direct learning) and group of mathematical initial ability (high, average, and low) to the enhancement of mathematical understanding ability of preservice mathematics teachers.