Thanks to its high density and long durability, synthetic DNA has been widely considered as a promising solution to the data explosion problem. However, due to the large amount of random base insertion-deletion-substitution (IDSs) errors from sequencing, reliable data recovery remains a critical challenge, which hinders its large-scale application. Here, we propose a modulation-based DNA storage architecture. Experiments on simulation and real datasets demonstrate that it has two distinct advantages. First, modulation encoding provides a simple way to ensure the encoded DNA sequences comply with biological sequence constraints (i.e., GC balanced and no homopolymers); Second, modulation decoding is highly efficient and extremely robust for the detection of insertions and deletions, which can correct up to ~40% errors. These two advantages pave the way for future high-throughput and low-cost techniques, and will kickstart the actualization of a viable, large-scale system for DNA data storage.