High dynamic range (HDR) video offers a more realistic visual experience than standard dynamic range (SDR) video, while introducing new challenges to both compression and transmission. Rate control is an effective technology to overcome these challenges, and ensure optimal HDR video delivery. However, the rate control algorithm in the latest video coding standard, versatile video coding (VVC), is tailored to SDR videos, and does not produce well coding results when encoding HDR videos. To address this problem, a data-driven λ-domain rate control algorithm is proposed for VVC HDR intra frames in this paper. First, the coding characteristics of HDR intra coding are analyzed, and a piecewise R-λ model is proposed to accurately determine the correlation between the rate (R) and the Lagrange parameter λ for HDR intra frames. Then, to optimize bit allocation at the coding tree unit (CTU)-level, a wavelet-based residual neural network (WRNN) is developed to accurately predict the parameters of the piecewise R-λ model for each CTU. Third, a large-scale HDR dataset is established for training WRNN, which facilitates the applications of deep learning in HDR intra coding. Extensive experimental results show that our proposed HDR intra frame rate control algorithm achieves superior coding results than the state-of-the-art algorithms. The source code of this work will be released at https://github.com/TJU-Videocoding/WRNN.git.