Recently, a variable-rate image compression conditioned on a pixel-wise quality map achieved an outstanding rate-distortion trade-off compared to the approaches based on multiple models. However, it is hard to find an appropriate pixel-wise quality map for the target rate, and the hyperprior is only used to capture the probability distribution of latent representation, which causes its inefficient utilization. In this paper, we propose a variable-rate image compression network with shallow to deep hyperprior trained with a uniform quality map generated by the trade-off parameter $\lambda$ of the rate-distortion optimization. The shallow to deep hyperprior structure enables the shallow hyperprior to improve the reconstruction image quality by compensating the latent representation as side information while estimating its distribution. Inspired by the fact that a uniform quality map can continuously scale the latent representations with the continuous change of $\lambda$ , we build an individual $R$ - $\lambda$ model, which characterizes the relation between R and $\lambda$ . With this $R$ - $\lambda$ model, we can perform precise and continuous rate control in the compression. To the best of our knowledge, this $R$ - $\lambda$ model is the first work to propose a continuous rate control for variable-rate learning-based image compression. Meanwhile, benefiting from the uniform values of the map, our method can handle various distortion metrics, such as MS-SSIM. Extensive experimental results show that the proposed model has achieved SOTA compression performance in variable-rate learning-based methods, achieving comparable compression performance compared with VVC. Furthermore, the rate control of our scheme shows very high accuracy.