DNA computing is a new computation form based on DNA biochemical reactions, which is mainly composed of sticker and splicing computation models. In this work, a microfluidic chip-based approach was established for splicing model-based DNA computing. A finite automaton with two input symbols (a, b) and three states (S0, S1, and S2) was applied in the pattern recognition for isosceles triangles. The DNA computation processes of automaton were realized through DNA digestion, ligation, DNA separation, and detection on the microfluidic chip. The established approach is efficient, controllable, and easy to integrate, which paves the way for the building of complete biomolecular computers in the future.