Sign language transition generation seeks to convert discrete sign language segments into continuous sign videos by synthesizing smooth transitions. However,most existing methods merely concatenate isolated signs, resulting in poor visual coherence and semantic accuracy in the generated videos. Unlike textual languages,sign language is inherently rich in spatial-temporal cues, making it more complex to model. To address this,we propose StgcDiff, a graph-based conditional diffusion framework that generates smooth transitions between discrete signs by capturing the unique spatial-temporal dependencies of sign language. Specifically, we first train an encoder-decoder architecture to learn a structure-aware representation of spatial-temporal skeleton sequences. Next, we optimize a diffusion denoiser conditioned on the representations learned by the pre-trained encoder, which is tasked with predicting transition frames from noise. Additionally, we design the Sign-GCN module as the key component in our framework, which effectively models the spatial-temporal features. Extensive experiments conducted on the PHOENIX14T, USTC-CSL100,and USTC-SLR500 datasets demonstrate the superior performance of our method.