A gas turbine shroud and platform seal system, which is constructed so that the flow of sealing air does not disturb a combustion gas flow, and thus any aerodynamic loss is reduced. The leaking air (60) leaks from between a platform (2) of moving blade (1) and an inside shroud (12) in a stationary blade (11). At a front or upstream side of the moving blade (1), the leaking air (60) flows along a S-shaped path within a space (8, 17) formed by a projecting end portion (12b) of the shroud, a honeycomb seal (14) and a projecting portion (4) of the platform. The air eventually flows out in the same flow direction as that of the combustion gas (50) along a surface of the platform (2). At a rear side of the moving blade (1), the leaking air (60) flows along an S-shaped path within a space (6, 9) formed by a projecting end portion (2b) of the platform, a projecting end portion (12b) of the shroud, a honeycomb seal (13) and a seal plate (3). The air eventually flows out in the same direction as that of the combustion gas (50) along a surface of the shroud (12). The air (60) flows in the same direction as the combustion gas (50), and thus a flow loss is reduced. Also, the air is not easily leaked, and a cooling effect of the platform and the shroud is increased due to a film cooling effect.