In this paper, a rate control scheme for screen content video coding is proposed for the Versatile Video Coding (VVC) standard. In view of the critical challenges arising from the spatial and temporal unnaturalness of screen content sequences, the proposed method relies on the specifically designed pre-analysis such that the content information regarding the scene complexity can be obtained. As such, the estimated residual complexity is then incorporated into the proposed complexity-aware rate models and distortion models, leading to the optimal bit allocations for each frame and coding tree unit (CTU). In particular, the optimization problem can be analytically solved with the proposed models, and the coding parameters such as Lagrangian multiplier λ and quantization parameter of each frame and CTU could be delicately derived according to the allocated bits through the proposed analytical models. Extensive experiments have been conducted to evaluate the effectiveness of the proposed method. Compared to the default hierarchical λ-domain rate control and other screen content rate control algorithms, the proposed method could achieve obvious RD performance gain, and the bit-rate accuracy could be improved.