A high-precision simulation method for gas-liquid two-phase flows on unstructured meshes has been developed as a part of numerical studies on a gas entrainment phenomenon in the sodium-cooled fast reactor (JSFR). In this study, a two-dimensional unstructured adaptive mesh algorithm is developed because an adaptive mesh technique is necessary to simulate the local gas entrainment phenomenon accurately in large size JSFR. In a proposed two-dimensional adaptive mesh algorithm, each cell is isotropically subdivided to reduce distortions of the mesh. In addition, a connection cell is formed to eliminate the edge incompatibility between a refined and a non-refined cells. When forming connection cells, patterns of each connection cell is determined by subdivision condisions of neighboring cells. After checking the developed two-dimensional unstructured adaptive mesh manipulations (subdivision and merging of cells and construction of connection cells), the present adaptive mesh algorithm is verified by solving well-kwon driven cavity problem. As the result, the present unstructured adaptive mesh algorithm succeeds in reproducing vortical flow field in the cavity using relatively small cell number.