Synthesizing multi-phase contrast-enhanced CT (CE-CT) images is clinically significant, as it can mitigate clinical risks such as radiation exposure and allergic reactions to contrast agents. However, existing methods treat multi-phase synthesis as separate tasks, failing to maintain the inter-phase dependencies and consistency between synthesized multi-phase CE-CT images. Moreover, the limited variability in CT intensity distributions makes it challenging to capture subtle variations in multi-phase imaging. For the first time, we propose a novel Causality-driven Spatio-temporal Generator (CSGen) for synthesizing multi-phase CE-CT imaging through three key novelties: 1) Using a novel phase-causality to creatively exploit the multi-phase variation content for driving the multi-phase CE-CT synthesizing, addressing the challenge of capturing multi-phase discriminative features through one model. 2) Introducing a new Spatio-temporal Transformer to establish the spatio-temporal correlation between multi-phase CE-CT images for leveraging multi-phase inter- and intra-dependencies and improving synthesis quality. 3) Multi-phase adversarial learning is designed for enhancing multi-phase discriminative feature learning. Experimental results (mean PSNR: 31.15, mean SSIM: 0.9066, mean NMAE: 3.17) demonstrate that CSGen outperforms state-of-the-art synthesis methods, and, for the first time, successfully synthesizes multi-phase CE-CT images.