Multi-field packet classification has evolved from traditional fixed 5-tuple matching to flexible matching with arbitrary combination of numerous packet header fields. For example, the recently proposed OpenFlow switching requires classifying each packet using up to 12-tuple packet header fields. It has become a great challenge to develop scalable solutions for next-generation packet classification that support higher throughput, larger rule sets and more packet header fields. This paper exploits the abundant parallelism and other desirable features provided by current field-programmable gate arrays (FPGAs), and proposes a decision-tree-based, 2-D multi-pipeline architecture for next-generation packet classification. We revisit the techniques for traditional 5-tuple packet classification and propose several optimization techniques for the state-of-the-art decision-tree-based algorithm. Given a set of 12-tuple rules, we develop a framework to partition the rule set into multiple subsets each of which is built into an optimized decision tree. A tree-to-pipeline mapping scheme is carefully designed to maximize the memory utilization while sustaining high throughput. The implementation results show that our architecture can store either 10K real-life 5-tuple rules or 1K synthetic 12-tuple rules in on-chip memory of a single state-of-the-art FPGA, and sustain 80 and 40 Gbps throughput for minimum size (40 bytes) packets, respectively.