Handwritten signature has long been a widely accepted biometric and applied in many verification scenarios. However, automatic signature verification remains an open research problem, which is mainly due to three reasons. 1) Skilled forgeries generated by persons who imitate the original writting pattern are very difficult to be distinguished from genuine signatures. It is especially so in the case of offline signatures, where only the signature image is captured as a feature for verification. 2) Most state-of-the-art models are writer-dependent, requiring a specific model to be trained whenever a new user is registered in verification, which is quite inconvenient. 3) Writer-independent models often have unsatisfactory performance. To this end, we propose a novel metric learning based method for offline writer-independent signature verification. Specifically, a dual triplet loss is used to train the model, where two different triplets are constructed for random and skilled forgeries, respectively. Experiments on three alphabet datasets — GPDS Synthetic, MCYT and CEDAR — show that the proposed method achieves competitive or superior performance to the state-of-the-art methods. Experiments are also conducted on a new offline Chinese signature dataset — CSIG-WHU, and the results show that the proposed method has a high feasibility on character-based signatures.