Abstract: A parallel full implicit Navier-Stokes solver based on weakly imposed wall boundary condition is proposed. First, a weak boundary procedure for viscous solid wall is implemented on the unstructured node-centered finite volume method. Upon this procedure, the corresponding viscous Jacobian is derived. Compared to the traditional strongly imposed wall boundary condition, the application of weakly imposed boundary condition eases the derivation. To address the issues of convergence and positivity preserving difficulties with regard to the Spalart-Allmaras (S-A) model, an unconditionally positive-convergent (UPC) implicit scheme for the S-A model using weakly imposed wall boundary condition is presented, which is based on the construction of a special implicit matrix to ensure both the convergence of the S-A model and the positivity of the turbulence working variables. The linear equations resulted from the full implicit time integration and the UPC scheme are solved using multicolor Gauss-Seidel iteration (MCGS) and MPI is employed for parallelization. The proposed approach is tested by simulating several two-dimensional and three-dimensional cases. Results from the numerical simulations demonstrate that:1) with larger penalty strength parameter, the results of weak boundary conditions tend to those of strong boundary conditions; 2) the weak boundary conditions satisfy flux consistency for force computation automatically, and therefore no special treatment is required.