An efficient parallelizable preconditioner for solving large-scale computations is presented. It is adapted to coarse-grain parallelism and can be used for both shared and distributed-memory parallel computers. The proposed preconditioner consists of several approximations of the system matrix. The first one is a block-diagonal, fully parallelizable approximation of the given system. The following matrices are coarser approximations of it, obtained trough an algebraic multi-grid strategy. The process is fully automatic and general and is solely based on information contained in the matrix and not on geometric domain decomposition techniques. The preconditioner is used to compute the steady solution of the compressible Navier-Stokes equations for subsonic laminar flows, on shared-memory computers, for a moderate number of processors. The multilevel preconditioner is robust and has a large potential for parallelism. Interesting savings in computational time for parallel computations are obtained when comparing the two-level preconditioner with the well-known incomplete Gaussian factorization.