A new high-resolution hybrid implicit scheme for solving the unsteady Euterflow equations to abtain steady solutions is provided in curvilinear coordinates. This scheme is mainly based on Steger-Warming' s implicit flux vector splitting technique and Harten' s numerical flux fura tion. With the hybrid scheme

we obtain the discrctized linear system with diagonally dominant coeff ctent matrix which enhances the convergence rate by use of the Line Gauss-Seidel relaxation procedure including backward and forward sweeps.The numerical procedures were applied to three examples for steady transonic flows in a channel. Computational results shows the convergence rate is very high due to the very big time steps. The scheme is capable of obtaining weak solutions for system of hyperbolic conservation equations. It also can exclude expansion shocks and lead only to physically relevant solutions. The new algorithm reaches steady shock solutions on the-grid with a one or two point monotone transition.