Computing connected components is a core operation on graph data. Since billion-scale graphs cannot be resident in memory of a single server, several approaches based on distributed machines have recently been proposed. The representative methods are Hash-To-Min and PowerGraph. Hash-To-Min is the state-of-the art disk-based distributed method which minimizes the number of MapReduce rounds. PowerGraph is the-state-of-the-art in-memory distributed system, which is typically faster than the diskbased distributed one, however, requires a lot of machines for handling billion-scale graphs. In this paper, we propose an I/O efficient parallel algorithm for billion-scale graphs in a single PC. We first propose the Disk-based Sequential access-oriented Parallel processing (DSP) model that exploits sequential disk access in terms of disk I/Os and parallel processing in terms of computation. We then propose an ultra-fast disk-based parallel algorithm for computing connected components, DSP-CC, which largely improves the performance through sequential disk scan and page-level cache-conscious parallel processing. Extensive experimental results show that DSP-CC 1) computes connected components in billion-scale graphs using the limited memory size whereas in-memory algorithms can only support medium-sized graphs with the same memory size, and 2) significantly outperforms all distributed competitors as well as a representative disk-based parallel method.