The temperature of high-power lithium-ion batteries has a great influence on their performance, safety, and stability; thus the battery thermal management system (BTMS) is a key component of electric vehicles. In this paper, a novel liquid-cooling BTMS with a thin plate and a slender tube is proposed for prismatic batteries, four different cooling structures of the tube are designed to achieve a high temperature uniformity, and a three-dimensional numerical model is established. The effects of different cooling structures, battery discharge rates, coolant inlet velocities and inner diameters of the slender tube on the thermal performance are investigated. The results indicate that design S3, for which the length of the effective heat transfer tube distributed by each battery increases gradually along the flow direction of the coolant, exhibits the best thermal management performance among the four designed cooling structures, especially in terms of the temperature uniformity. When the inner diameter of the slender tube is 2 mm and the inlet velocity is not less than 0.5 m/s, the maximum temperature difference between the batteries is reduced to 4.23 degrees C at a 2C discharge rate. This study can provide guidance for the structural design of BTMSs for prismatic batteries.