This paper describes subspace constrained feature space maximum likelihood linear regression (FMLLR) for rapid adaptation. The test speaker’s FMLLR rotation matrix is decomposed into the product of two triangular matrices which are restricted to lie in two subspaces spanned by upper and lower triangular matrix basis. The basis matrices could be obtained from training speaker’s FMLLR matrices by maximum likelihood (ML) transformation selection and then LU decomposition with available adaptation data. The basis weights could be estimated efficiently by solving two convex optimization problems alternatively aiming to maximize the likelihood of adaptation data. Experimental results show that the method could get significant improvement over full MLLR and Eigenspace-based MLLR[1] while keeping advantages of FMLLR for rapid adaptation in ASR application for car-navigation.