Mathematical problems can be divided into two types, namely, process-open and process-constrained problems. Solving these two types of problems may require different cognitive mechanisms. However, there has been only one study that investigated the differences of the cognitive abilities in process-open and process-constrained problem solving, and these researchers did not consider the influence of other closely related cognitive abilities. Therefore, in the current study we aimed to investigate the different cognitive mechanisms for process-open and process-constrained problem solving while controlling for related cognitive abilities. For this study we recruited 336 fifth grade students (mean age = 10.73 ± 0.32 years old). The results showed that after controlling for age, gender, and other cognitive abilities, inductive reasoning (measured by nonverbal matrix reasoning) contributes only to process-open problem solving; language comprehension (measured by sentence comprehension) contributes only to process-constrained problem solving; spatial ability (measured by paper folding) contributes to both process-open and process-constrained problem solving; and executive function (measured by the Wisconsin card sort test) contributes to neither process-open nor process-constrained problem solving. These results suggest that cognitive abilities related to generating new information (e.g., inductive reasoning, spatial ability) might play an important role in process-open problem solving. In contrast, cognitive abilities related to retrieval prior knowledge (e.g., language comprehension, spatial ability) might play an important role in process-constrained problem solving. The current findings could promote the efficiency of learning and teaching by enabling the designing of different instruction for process-open and process-constrained problem solving according to students' cognitive characteristics.