This study explored 54 preservice elementary teachers' identification and modification of mathematical tasks in raising cognitive demand and examined the features of their modified tasks. The study collected data using a three-phase activity: (a) identifying the level of cognitive demand of the given task, (b) modifying the low cognitive demand tasks to higher ones, and (c) presenting anticipated student responses to the modified tasks. Through the inductive content analysis approach, the study revealed the following findings: (a) the participants were more successful in identifying lower-level tasks than higher-level ones; (b) the participants modified mainly three task features (task formats, response types, and complexity) to increase the level of cognitive demand of tasks, and more varied modification strategies were observed when the given task's level was the lowest; (c) the researchers' evaluation of the participants' modified tasks showed that their attempts did not always guarantee the change of the level of cognitive demand in some cases; (d) in some cases, the participants' anticipated student responses contained erroneous content, and story problems used in the modified tasks were unreasonable. This study contributed to understanding preservice teachers' competency in identifying the level of cognitive demand of mathematical tasks and their modification strategies and errors. The findings also offered implications for further discussions to be considered in mathematics teacher education.