Third-order hybrid reconstructed methods based on the combination of least-squares recovery and reconstruction were developed for solving compressible laminar and turbulent flows to improve the calculation efficiency of the discontinuous Galerkin methods and overcome the deficiency of the least-squares reconstruction in satisfying the two-exact property. Navier-Stokes equations and the modified equation of the negative Spalart-Allmaras model were coupled as the equation system and solved using the developed third-order reconstructed discontinuous Galerkin methods. The lower-upper symmetric Gauss-Seidel preconditioning generalized minimal residual method based on the semianalytical exact Jacobian matrix and the fourth-order implicit Runge-Kutta method were implemented in temporal advance. Harten-Lax-van Leer contact and second Bassi-Rebay (BR2) schemes were adopted to calculate the inviscid and viscous terms, respectively. Third-order reconstruction was applied to solve the local and global lifting operators of the BR2 scheme, improving the calculation accuracy. The benchmarks were selected to verify the accuracy and calculation efficiency of the developed rDGP₁P₂ method. The research results indicate that the developed reconstructed rDGP₁P₂ methods have high computational accuracy and efficiency.