Multimodal large language models (MLLMs) have demonstrated impressive capabilities across various vision-language tasks. However, a generalist MLLM typically underperforms compared with a specialist MLLM on most VL tasks, which can be attributed to task interference. In this paper, we propose a mixture of multimodal experts (MoME) to mitigate task interference and obtain a generalist MLLM. Our MoME is composed of two key components, a mixture of vision experts (MoVE) and a mixture of language experts (MoLE). MoVE can adaptively modulate the features transformed from various vision encoders, and has a strong compatibility in transformation architecture. MoLE incorporates sparsely gated experts into LLMs to achieve painless improvements with roughly unchanged inference costs. In response to task interference, our MoME specializes in both vision and language modality to adapt to task discrepancies. Extensive experiments show that MoME significantly improves the performance of generalist MLLMs across various VL tasks.