In engineering practice, the system of the one- or two-equation turbulence model together with Reynolds-averaged Navier-Stokes (RANS) equations is decoupled during its solving, which is known as loosely coupled solving. In the process, RANS equations and turbulence model equations are commonly solved separately with different numerical methods, which may easily incur additional numerical dissipation due to inconsistent calculation accuracy. In order to eliminate this dissipation, RANS equations and Spalart-Allmaras model equation are hereby coupled into one strongly coupled system of equations, and an efficient method is developed for its solution. The convective terms are discrete by the Roe scheme, and the time derivative terms are discrete by the LU-SGS (Lower-Upper Symmetric-Gauss-Seidel) method. In order to accelerate the convergence, a three level V-cycle multigrid algorithm is used. Through numerical experiments of the airfoil/wing and oscillating airfoil/wing, the convergence and accuracy of this algorithm are verified, and results show that its accuracy is significantly better than the loosely coupled algorithm, especially in the prediction of drag force.