A turbine through flow design approach based on time-marching method (TMM) with a novel radial secondary loss redistribution model has been developed. The through flow TMM solves two dimensional (2D) Euler equations in body fitted curvilinear coordinate. The TMM numerical scheme is the third order Godunov scheme with the total variation diminishing (TVD) property. The semi-implicit Crank-Nicolson scheme is used in temporal direction. The S2 stream surface is modeled by a quadratic function of axial coordinate to construct computational domain. Profile, secondary and tip clearance leakage losses are considered in the loss models. The secondary loss is broken down into the boundary layer and passage vortex core losses. A three stage low pressure turbine is designed and studied by the through flow TMM. Three dimensional (3D) computational fluid dynamics (CFD) software is used to check the design results. The study shows that the absolute values of through flow calculation errors of turbine mass flow rate, expansion ratio and isentropic efficiency are 2.04%, 0.040 and 0.0049. The aerodynamic parameter radial variance trends of the through flow results are reliable. The loss redistribution model can reflect the loss increment near endwalls and the loss peaks at passage vortex core locations.