Real-time speech conversation is essential for natural and efficient human-machine interactions, requiring duplex and streaming capabilities. Traditional Transformer-based conversational chatbots operate in a turn-based manner and exhibit quadratic computational complexity that grows as the input size increases. In this paper, we propose DuplexMamba, a Mamba-based end-to-end multimodal duplex model for speech-to-text conversation. DuplexMamba enables simultaneous input processing and output generation, dynamically adjusting to support real-time streaming. Specifically, we develop a Mamba-based speech encoder and adapt it with a Mamba-based language model. Furthermore, we introduce a novel duplex decoding strategy that enables DuplexMamba to process input and generate output simultaneously. Experimental results demonstrate that DuplexMamba successfully implements duplex and streaming capabilities while achieving performance comparable to several recently developed Transformer-based models in automatic speech recognition (ASR) tasks and voice assistant benchmark evaluations. Our code and model are released.