An experimental study using the combustor with branch tube was conducted in order to model the industry combustor with FGR (flue gas recirculation) system and to study a thermo-acoustic instability generated by a branch tube. The branch tube is a structure used to modify a system geometry and then to change its pressure field, and the thermo-acoustic instability, usually occurs in a confined geometry, can result in serious problems on industrial combustors. Thus understanding of the instability created by modifying geometry of combustor is necessary to design and operate combustor with FGR system. Pressure fluctuation in the combustion chamber was observed according to diameter and length of branch and it was compared with the solution of 1-D wave equation. It was found that branch tube affects the pressure field in the combustion chamber, and the pressure fluctuation in the combustion chamber was reduced to almost zero when phase difference between an incipient wave in the combustion chamber and a reflected wave in the branch tube is $pi$ at the branch point. Also, the reduction of pressure fluctuation is irrespective of the installed height of branch tube if it is below $h^*=0.9$ in the close-open tube and open-open tube.