To improve the structural safety of LNG plate-fin heat exchanger, the analysis model on stress of plate-fin structures was established based on thermal-elastic theory. The stress characteristics of plate-fin structures at different brazed joints were analyzed by thermal-stress coupling method. Results showed that the maximum equivalent stress reached the peak value at the brazed joint near fin and plate side when the curvature radius of the brazing angle was 0.5 mm and the fusion distance was 0.137 5 mm, which was mainly induced by the maximum normal stress. The equivalent stress, the maximum normal stress, and the maximum shear stress changed steadily at the brazing seam. The equivalent stress of the brazed joints near fin and plate side increased with the increment of curvature radius on brazing arc. The stress concentration at brazed joints was reduced with the decrease of the curvature radius. The equivalent stress at the brazed joints near plate side decreased when the fusion distance on brazing arc increased, while it was opposite at the brazed joints near fin side. The equivalent stress of the brazed joints near plate side was larger than that near the fin side when the fusion distance on brazing arc was less than 0.08 mm. The above research results provide theoretical basis for the design, manufacture, and operation of LNG plate-fin heat exchangers in large LNG plants.