The low lying rotational resonance states of Ar-HCl van der Waals molecule in the vibrational ground state of HCl are calculated for several total angular momentum states within the model of a rigid rotor-atom system. The necessary scattering calculations are done by the finite range scattering wave function (FRSW) method [J. Chem. Phys. 99, 1057 (1993)] adopting energy independent auxiliary functions which makes the scattering calculations at many energies much more efficient. Discrete eigenvectors and eigenvalues of Hamiltonian matrix are calculated on a finite range via the successive diagonalization-truncation scheme combined with the discrete variable representation (DVR). Analytical eigenfunctions of the asymptotic Hamiltonian operator in a body-fixed frame excluding only the interaction potential, but including all the effective centrifugal potential terms, are used as asymptotic wave functions, which reduces the dynamical range required for the L(2) scattering calculations. After a single diagonalization of the Hamiltonian in the finite range L(2) representation, resonance parameters are extracted through the energy dependence of Smith’s lifetime matrix. A search algorithm for multiple resonances is used assuming constant background effects and isolated, simple resonances. Several recommendations for the choice of the translational basis functions and the basis set ranges which target specific kinds of resonances with various accuracies are given. Resonance energies and widths (lifetimes and partial decay probabilities) for many predissociating states of Ar-HCl are given with unprecedental accuracy.