Domain-specific Multi-modal Neural Machine Translation (DMNMT) aims to translate domain-specific sentences from a source language to a target language by incorporating text-related visual information. Generally, domain-specific text-image data often complement each other and have the potential to collaboratively enhance the representation of domain-specific information. Unfortunately, there is a considerable modality gap between image and text in data format and semantic expression, which leads to distinctive challenges in domain-text translation tasks. Narrowing the modality gap and improving domain-aware representation are two critical challenges in DMNMT. To this end, this paper proposes a progressive modality-complement aggregative MultiTransformer, which aims to simultaneously narrow the modality gap and capture domain-specific multi-modal representation. We first adopt a bidirectional progressive cross-modal interactive strategy to effectively narrow the text-to-text, text-to-visual, and visual-to-text semantics in the multi-modal representation space by integrating visual and text information layer-by-layer. Subsequently, we introduce a modality-complement MultiTransformer based on progressive cross-modal interaction to extract the domain-related multi-modal representation, thereby enhancing machine translation performance. Experiment results on the Fashion-MMT and Multi-30k datasets are conducted, and the results show that the proposed approach outperforms the compared state-of-the-art (SOTA) methods on the En-Zh task in E-commerce domain, En-De, En-Fr and En-Cs tasks of Multi-30k in general domain. The in-depth analysis confirms the validity of the proposed modality-complement MultiTransformer and bidirectional progressive cross-modal interactive strategy for DMNMT.