In this paper we propose a partial parsing model which achieves robust parsing with a large HPSG grammar. Constraint-based precision grammars, like the HPSG grammar we are using for the experiments reported in this paper, typically lack robustness, especially when applied to real world texts. To maximally recover the linguistic knowledge from an unsuccessful parse, a proper selection model must be used. Also, the efficiency challenges usually presented by the selection model must be answered. Building on the work reported in Zhang et al. (2007a), we further propose a new partial parsing model that splits the parsing process into two stages, both of which use the bottom-up chart-based parsing algorithm. The algorithm is implemented and a preliminary experiment shows promising results.