This paper presents a novel approach, termed {\em Temporal Latent Residual Network (TLRN)}, to predict a sequence of deformation fields in time-series image registration. The challenge of registering time-series images often lies in the occurrence of large motions, especially when images differ significantly from a reference (e.g., the start of a cardiac cycle compared to the peak stretching phase). To achieve accurate and robust registration results, we leverage the nature of motion continuity and exploit the temporal smoothness in consecutive image frames. Our proposed TLRN highlights a temporal residual network with residual blocks carefully designed in latent deformation spaces, which are parameterized by time-sequential initial velocity fields. We treat a sequence of residual blocks over time as a dynamic training system, where each block is designed to learn the residual function between desired deformation features and current input accumulated from previous time frames. We validate the effectivenss of TLRN on both synthetic data and real-world cine cardiac magnetic resonance (CMR) image videos. Our experimental results shows that TLRN is able to achieve substantially improved registration accuracy compared to the state-of-the-art. Our code is publicly available at https://github.com/nellie689/TLRN.