This paper proposes an optimal day-ahead optimization schedule for gas-electric integrated energy system (IES) considering the bi-directional energy flow. The hourly topology of electric power system (EPS), natural gas system (NGS), energy hubs (EH) integrated power to gas (P2G) unit, are modeled to minimize the day-ahead operation cost of IES. Then, a second-order cone programming (SOCP) method is utilized to solve the optimization problem, which is actually a mixed integer nonconvex and nonlinear programming issue. Besides, cutting planes are added to ensure the exactness of the global optimal solution. Finally, simulation results demonstrate that the proposed optimization schedule can provide a safe, effective and economical day-ahead scheduling scheme for gas-electric IES.