Spatiotemporal dynamic Electrical Impedance Tomography (EIT) is an emerging non-invasive imaging technique that reconstructs internal structures by measuring tissue conductivity distributions. This study utilizes the tensor nuclear norm (TNN) method based on tensor singular value decomposition (t-SVD) to leverage low-rank and sparse priors for capturing spatiotemporal characteristics, overcoming the limitations of traditional EIT algorithms in dynamic imaging. The alternating direction method of multipliers (ADMM) is employed to solve the optimization problem, emphasizing spatiotemporal continuity and achieving precise reconstruction of dynamic conductivity changes. Simulations and experiments, particularly in lung respiration imaging, demonstrate the superior performance of the TNN method compared to the conjugate gradient least squares (CGLS) method. Results show that TNN excels in noise reduction and image continuity, providing a novel approach for dynamic EIT monitoring applications.