The issue of a single point of failure has grown increasingly severe due to the widespread adoption of blockchain systems and voting protocols. Fortunately, threshold cryptography can solve this problem by distributing the key storage. However, a key issue of such a scheme is how to generate a secret shared by all participants without revealing their secrets. Most solutions are based on a trusted third party, while a few solutions rely on all participants together. The first approach imposes significant demands on the third party, making its implementation challenging and resource-intensive. The second method, known as distributed key generation (DKG), operates without relying on a trusted third party, offering a more efficient and decentralized solution. Compared with existing DKG protocols which rely on cryptographic foundations such as discrete logarithm problems and bilinear pairings, lattice-based cryptography offers notable benefits, including superior efficiency and quantum resistance, making it a promising alternative. Recognizing these advantages, we proposed a module-lattice-based DKG (MDKG) scheme based on zero-knowledge proofs. Our MDKG scheme does not require broadcasting shared secrets between users, satisfying the security requirements of robust correctness and secrecy, and can resist quantum attacks. Experiments show that our MDKG scheme reduces the secret sharing size by 74% and reduces the time cost by at least 90% compared to the existing lattice-based DKG scheme.