With the rapid increase of available digital data, DNA storage is identified as a storage media with high density and capability of long-term preservation, especially for archival storage systems. However, the encoding density (i.e., how many binary bits can be encoded into one nucleotide) and error handling are two major factors intertwined in DNA storage. Considering encoding density, theoretically, one nucleotide can encode two binary bits (upper bound). However, due to biochemical constraints and other necessary information associated with payload, the encoding densities of various DNA storage systems are much less than this upper bound. Additionally, all existing studies of DNA encoding schemes are based on static analysis and really lack the awareness of dynamically changed digital patterns. Therefore, the gap between the static encoding and dynamic binary patterns prevents achieving a higher encoding density for DNA storage systems. In this paper, we propose a new Digital Pattern-Aware DNA storage system, called DP-DNA, which can efficiently store digital data in DNA storage with high encoding density. DP-DNA maintains a set of encoding codes and uses a digital pattern-aware code (DPAC) to analyze the patterns of a binary sequence for a DNA strand and selects an appropriate code for encoding the binary sequence to achieve a high encoding density. An additional encoding field is added to the DNA encoding format, which can distinguish the encoding scheme used for those DNA strands, and thus we can decode DNA data back to its original digital data. Moreover, to further improve the encoding density, a variable-length scheme is proposed to increase the feasibility of the coding scheme with a high encoding density. Finally, the experimental results indicate that the proposed DP-DNA achieves up to 103.5% higher encoding densities than prior work.