Large-capacity pulse-tube coolers are considered promising candidates for applications in high-temperature superconductivity technology, small gas liquefiers, and cryogenic storage tanks. This paper introduces a novel shell-tube heat exchanger particularly designed for such a cooler. In one heat-transfer subunit of this configuration, several small-diameter copper tubes are welded inside a large-diameter tube. This heat exchanger is characterized by small hydraulic diameter, high porosity and uniform gas temperature distribution. To verify its performance, a numerical simulation was first carried out to compare the temperature distributions of the shell-tube and plated-fin configurations. Experiments were then conducted to investigate their cooling performance. According to the experimental results, the shell-tube heat exchanger achieved better heat-transfer performance, especially with large input power. The gas temperature at the inlet of the heat exchanger and the temperature gradient in the regenerator were significantly decreased in the novel shell-tube design, which further demonstrated its better performance.