Despite the unprecedented compression efficiency achieved by deep learned image compression (LIC), existing methods usually approximate the desired bitrate by adjusting a single quality factor for a given input image, which may compromise the rate control results. Considering the Rate-Distortion (R - D) characteristics of different spatial content, this work introduces the block-level rate control based on a novel D - {\lambda} model specific for LIC. Furthermore, we try to exploit the inter-block correlations and propose a block-wise R - D prediction algorithm which greatly speeds up block-level rate control while still guaranteeing high accuracy. Experimental results show that the proposed rate control achieves up to 100 times, speed-up with more than 98% accuracy. Our approach provides an optimal bit allocation for each block and therefore improves the overall compression performance, which offers great potential for block-level LIC.