Generative Pre-trained Transformer (GPT) models have achieved remarkable performance on various natural language processing tasks, and have shown great potential as backbones for audio-and-text large language models (LLMs). Previous mainstream audio-and-text LLMs use discrete audio tokens to represent both input and output audio; however, they suffer from performance degradation on tasks such as automatic speech recognition, speech-to-text translation, and speech enhancement over models using continuous speech features. In this paper, we propose LauraGPT, a novel unified audio-and-text GPT-based LLM for audio recognition, understanding, and generation. LauraGPT is a versatile LLM that can process both audio and text inputs and generate outputs in either modalities. We propose a novel data representation that combines continuous and discrete features for audio: LauraGPT encodes input audio into continuous representations using an audio encoder and generates output audio from discrete codec codes. We propose a one-step codec vocoder to overcome the prediction challenge caused by the multimodal distribution of codec tokens. We fine-tune LauraGPT using supervised multi-task learning. Extensive experiments show that LauraGPT consistently achieves comparable to superior performance compared to strong baselines on a wide range of audio tasks related to content, semantics, paralinguistics, and audio-signal analysis, such as automatic speech recognition, speech-to-text translation, text-to-speech synthesis, speech enhancement, automated audio captioning, speech emotion recognition, and spoken language understanding.