Rate control plays an essential role in real video applications due to the limitation of the bandwidth and storage budget. Supported by reference picture resampling (RPR) in Versatile Video Coding (VVC), which enables resolution changes without introducing an intra-coded frame, it is possible to adjust picture resolutions to adapt to the required bit-rate. However, few rate control algorithms with resolution changes have been explored for VVC. Therefore, we propose a λ-domain rate control algorithm with resolution changes in this paper. In the proposed rate control scheme, the coding resolution of one frame is determined based on the property of the frame. To make the rate control scheme adaptive to mixed resolutions, the rate control parameters of the full resolution and the low resolution are updated separately. Furthermore, λ and QP of the frames with different resolutions are unified to obtain appropriate coding parameters. Simulation results show that a BD-rate coding gain about 3.7% on average can be achieved with the reduction of computational complexity. Besides, negligible bitrate error can be observed at both sequence and frame level.