There is a strong relationship between field-dependent (FD), field-independent (FI) cognitive styles, and problem-solving performance. FD students are more oriented towards the outside world, while FI students rely more on their knowledge and experience. The present study aimed to reveal the position of the FI and FD student's errors in algebraic problem-solving. The subjects of this study were 27 students of class VII in one of the Junior High Schools in Kefamenanu, Indonesia, Academic Year 2018/2019. Data collection involved tests of algebraic problem-solving ability, interviews, and Group Embedded Figure Test. The case study results showed that the algebraic problem-solving abilities of FI students were better than FD students. The scores of algebraic problem-solving abilities of FI students were dominant in the medium and high categories. In contrast, the FD students were dominant in the medium and low categories. Also, FI students predominantly committed procedural errors. Whereas, most FD students made errors on all types of errors, specifically factual, conceptual, and procedural errors. Thus, it is recommended that FI and FD students' algebraic problem-solving ability become the focus of attention and importance to characterize them as a basis for further research.