In this paper, we address the limitations of existing text-to-image diffusion models in generating demographically fair results when given human-related descriptions. These models often struggle to disentangle the target language context from sociocultural biases, resulting in biased image generation. To overcome this challenge, we propose Fair Mapping, a general, model-agnostic, and lightweight approach that modifies a pre-trained text-to-image model by controlling the prompt to achieve fair image generation. One key advantage of our approach is its high efficiency. The training process only requires updating a small number of parameters in an additional linear mapping network. This not only reduces the computational cost but also accelerates the optimization process. We first demonstrate the issue of bias in generated results caused by language biases in text-guided diffusion models. By developing a mapping network that projects language embeddings into an unbiased space, we enable the generation of relatively balanced demographic results based on a keyword specified in the prompt. With comprehensive experiments on face image generation, we show that our method significantly improves image generation performance when prompted with descriptions related to human faces. By effectively addressing the issue of bias, we produce more fair and diverse image outputs. This work contributes to the field of text-to-image generation by enhancing the ability to generate images that accurately reflect the intended demographic characteristics specified in the text.